Hmm. If all of the backgrounds allowed for a campaign were roughly equivalent to the value of a feat and designed in such a way that they did not stack with other equivalent feats and were flexible enough that you weren't penalized for taking the stereotypical one for your class because you already had the benefit... it would still be power creep, but only one feat as a background for a campaign... would that be sufficient?
For example, if the article were instead:
(Predefining a feat
Skill Consistency
Prerequisite: Training in chosen skill
Benefit: Choose a skill in which you have training. You may reroll any check made with that skill, but you must take the second roll.
Special: You may take this feat more than once. Each time you select this feat, choose a different skill.)
Wandering Duelist: You gain one of Skill Training, Skill Focus, or Skill Consistency in Intimidate.
Scorned Noble: As written, but a +2 feat bonus.
Redemption Seeker: For both Diplomacy and Insight, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Seeker for the Lost Clan: For both History and Dungeoneering, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Warsmith: You gain the Enchant Magic Item and Disenchant Magic Item rituals, but working only on weapons and armor and usable from level 1 without the Ritual Caster feat. If you are also a ritual caster, you may perform them in half the time on weapons and armor. In addition, you may craft and repair normal weapons and armor at twice the normal speed or two days for a weapon or four days for armor, whichever is faster.
Brother in Battle: You gain one of Skill Training, Skill Focus, or Skill Consistency in Endurance.
Seducer: For both Bluff and Insight, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Magic Scholar: For both Arcana and History, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Eldritch Harlequin: For both Arcana and Thievery, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill. (Note: Bluff instead of Arcana in article, but given Con Artist and “Eldritch”, replacing Bluff with Arcana. Could swap Thievery for Bluff instead, but that would duplicate Cult Escapee)
Silent Hunter: For both Stealth and Perception, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Forest Warden: For both Nature and Perception, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Explorer/Guide: Gain one of Linguist, Skill Focus in Nature, or learn one language of your choice, add Nature to your class skill list, and gain a +2 feat bonus to Nature checks.
Merchant Prince: Gain one of Linguist, Skill Focus in Insight, or learn one language of your choice, add Insight to your class skill list, and gain a +2 feat bonus to Insight checks.
Detective: For both Insight and Perception, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Wandering Mercenary: As written.
Con Artist: For both Bluff and Thievery, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Street Urchin: For both Intimidate and Streetwise, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
River Smuggler: For both Athletics and Streetwise, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Cloistered Priest: You gain one of Skill Training, Skill Focus, or Skill Consistency in Religion.
Gritty Sergeant: You gain one of Weapon Proficiency, Weapon Focus, or Quick Draw.
Noble Scion: You gain one of Jack of All Trades, or either Skill Training or Skill Focus in a knowledge skill.
Scion of an Ancient Bloodline: You gain one of Skill Training, Skill Focus, or Skill Consistency in History.
Cult Escapee: For both Arcana and Bluff, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Young Cutthroat: For both Intimidate and Thievery, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Auspicious Birth: As written it is similar to toughness, but more frontloaded. It may be used as written, or alternatively: ‘Gain additional hit points equal to your highest ability bonus. At paragon tier, increase this amount to 4 + Bonus. At epic tier, increase this amount to 8 + Bonus.’ If more sources of hit points offend, consider ‘You gain one of Durable, Toughness, or a +3 feat bonus to death saves.’
Traveling Missionary: Gain one of Linguist, Skill Focus in Religion, or learn one language of your choice, add Religion to your class skill list, and gain a +2 feat bonus to Religion checks.
Recent Convert: As written.
Former Gladiator: As written. Duplicates Wandering Mercenary.
Haunted Veteran: As written.
Former Barbarian: You gain one of Skill Training, Skill Focus, or Skill Consistency in Nature.
Prison Conversion: You gain one of Skill Training, Skill Focus, or Skill Consistency in Streetwise.
Crusading Zealot: You gain a +2 feat bonus to saving throws until you fail a saving throw, and then the bonus is gone until you take an extended rest. (Note: +1 in article and only requires ‘a rest’)
Trained From Birth For A Specific Prophecy: You may reroll any initiative check. If you do so, you must take the second roll.
Last of the Breed: For both Endurance and Perception, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Monster Hunter: As written.
Fugitive from a Vengeful Rival: For both Bluff and Stealth, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Assassin: For both Arcana and Stealth, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Cat Burglar: For both Athletics and Thievery, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Political Rebel: For both Diplomacy and Streetwise, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
On the Run from the Devil: For both Bluff and Perception, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Apprentice of Sinister Cabal: For both Arcana and Dungeoneering, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Born Under a Bad Sign: See Auspicious Birth, which it amusingly duplicates.
Vet Who Can’t Let Go: For both History and Intimidate, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Noble Bred for War: You gain one of Weapon Proficiency, Weapon Focus, or Skill Focus in Diplomacy.
Officer Who Came Out of Retirement: You gain one of Improved Initiative, or either Skill Training or Skill Focus in History.
Arcane Student Who Saw Too Much: As written, but a +2 feat bonus. (Note: I realize some will object this as too powerful, but to be worth a feat it should at least not look like 1/10th as useful as Human Perseverance)
Missing Master: For both Insight and Perception, you either add the skill to your class list or gain a +2 feat bonus if it already is a class or trained skill.
Imbuer: You gain the Enchant Magic Item and Disenchant Magic Item rituals, but working only on implements and wondrous items and usable from level 1 without the Ritual Caster feat. If you are also a ritual caster, you may perform them in half the time on implements and wondrous items. In addition, you may craft and repair normal implements and wondrous items at twice the normal speed or two days for an implement or four days for a wondrous item, whichever is faster. (Note: Four days for any wondrous item? That seems odd, given the unbounded nature of wondrous items)
There are some of those backgrounds that feel too specific, not closely enough associated, and/or might be better not being a duplicate, such as Wandering Mercenary, Haunted Veteran, Trained from Birth for a Specific Prophecy, or Born Under a Bad Sign. I’d consider putting more options or work into each until it felt like there was a real choice associated, but my goal was to simply do a quick pass and reduce or improve each to be worth a feat. If backgrounds are about a feat in value, a DM can decide to let everyone have a bonus feat, allow people to pick up backgrounds later for the cost of a feat, and/or allow them as level 1 feats.