Faerie Fire isn't very good in tier 1, in fact I think I'll start a thread about that. Heat Metal is vastly overrated due to it's highly situational nature. Zone of Truth is harder to guage. It's never a spell I've though of as strong but I could be missing something. Bane is terrible in tier 1.
Speaking as someone who has played both Bard and Druid, and Wizard for that matter, but that's irrelevant for this point, Faerie Fire is amazing. Less so if you're using the optional rules for Flanking, but about half of the groups I've played in don't.
Even so, advantage is especially valuable in Tier 1, where combat classes have fewer attacks, and thus fewer chances to hit. And because both you and the enemy have fairly low hp pools, every turn someone isn't landing a hit makes a big difference (i.e. the difference between whether the enemy goes down, or you do).
And Heat Metal is good precisely because of the situations it's useful for. i.e. An enemy with Heavy Armor or a Greatsword. Fighting someone with either of these two things in Tier 1 is terrifying. If they have both, it can be a nightmare. Your melee combatants only have 1 attack per round, each to hit someone with 16-18 AC. And Greatswords hit like trucks when they're aimed at anyone but your Barbarian.
Blur, Enlarge/Reduce, Darkvision, Flaming Sphere, Levitate, Scorching Ray, Web, Spider Climb, fog cloud, thunderwave,
Half of these spells are terrible.
Blur is a worse Mirror Image in every way. And sure, you can stack them together, but that's two of your three 2nd level Spell Slots (assuming 4th level) and two of your 8-9 Prepared spells. If you're being threatened, just Misty Step. Or disengage. Or dash. Or break line of sight. Or do anything else that doesn't involve knowing, preparing, and casting Blur.
Enlarge/Reduce really isn't great, but it can be fun and does have some utility, so... take it or leave it. And I say this as someone who has taken this spell in the past and then never used it, because you have much better things you can do with your concentration and a 2nd Level Spell Slot.
Darkvision? I saw Darkvision on your list and I had to double-check that it wasn't a Ritual, because I cannot fathom spending a 2nd level Spell Slot to give someone Darkvision. It's certainly inconvenient when a character in the party doesn't have it, but that's what torches are for. Or the Light Cantrip. Not your precious few 2nd level Spell Slots.
Flaming Sphere is good, that's true. So is Web, albeit a bit overrated, as well as DM and party dependent. Basically, that type of Crowd Control becomes significantly less useful if your enemies act intelligently, or your allies act stupidly. Scorching Ray is fine, too. Personally, I go with Dragon's Breath cast on my Familiar.
Spider Climb/Levitate: In my experience, this is how you aggro every archer in an encounter. They can smell that potential fall damage. They're good utility spells, though, albeit expensive. Levitate, at least, can double as offensive CC that targets Con, so it's more worth Preparing than Spider Climb is.
Fog Cloud is great for anyone with Blindsense or Tremorsense, but that's infinitely more likely to be one of your enemies, then it is anyone in your party.
Thunderwave has three problems. The first is that it's centered on you. The second is that it can damage and push back your allies. And the third is that everything within 300 ft heard you. Oh no, I'm in a bit of a pinch! Time to aggro everything! KABOOM! (I guess there's a fourth problem, which is that it's also on the Bard's Spell List)
I'll tell you what. Make an actual level 3 bard. Tell me what spells he knows. I'll make a level 3 wizard then and we can compare the capabilities of each class. Trying to compare anything to an undefined spell caster is a pain.
Alright. That'll be a fun game. Let's assume an the average stat-line (which conveniently gives us an 18 in our respective primary stats at level 1).
16, 14, 13, 12, 10, 9
Valor Bard
Race: Half-Elf
Darkvision
Fey Ancestry: Advantage on Saves against Charms, and can't be put to Sleep.
Skill Versatility: Two extra Skill Proficiencies.
Ability Scores: Str 9 | Dex 15 | Con 14 | Int 10 | Wis 12 | Cha 18
HP: 24 [8+2d8(5+5)+(3*Con)]
AC: 17 [Chain Shirt + Shield + Dex)
Skill Proficiencies
Acrobatics +4 (Background)
Perception +3 (Background)
Perform +6 (Bard)
Persuasion +6 (Bard)
Deception +8 (Bard) -Expertise
Stealth +6 (Half-Elf) -Expertise
Survival +3 (Half-Elf)
Class Features
Spellcasting (2 Cantrips, 6 Spells Known)
Bardic Inspiration 4(d6)
Jack of All Trades (+1 to all non-proficient Skills)
Song of Rest (d6)
Expertise (Deception, Stealth)
Combat Inspiration (+Inspiration Dice to Damage or AC)
Spells Known
Cantrips: Minor Illusion, Vicious Mockery
1st Level: Faerie Fire, Healing Word, Dissonant Whispers, Disguise Self
2nd Level: Invisibility, Heat Metal
If there's already a healer in the party, replace Healing Word with Heroism or Tasha's.
If Sleep is still useful at Level 3 (as this build assumes that Sleep was traded away at Level 3), keep it instead of either Disguise Self or Invisibility.
Replace Heat Metal with Phantasmal Force if you fight more dangerous beasts, than people.