You like your group and the DM's stories and such; to me it seems like 'throwing the baby out with the bathwater' if this one Skill check thing makes you quite. One thing that 5e is excellent at, is opening up the flood gates for creative freedom in terms of making an interesting character. You have to think in terms of "character" more than "mechanics", however. The 5e system lets someone play an "intellectual fighter, always wanted to be a wizard but never had the opportunity and always forced into physical roles because of his natural strength and size"...without penalizing you.
5e has a "smaller numbers" thing, and it seems to be the basis of your disappointment in the skill stuff. You are simply not going to see "high numbers". So seeing someone without Proficiency with a +4 bonus, and looking at your Bard and seeing a +6 may not seem like a big bonus. But it actually is quite likey to make a difference...once your DM gets a more solid feel for setting DC's and such. My rule of thumb is "DC 10 for mundane; DC 12 for a bit odd; DC +++ as the more obscure stuff kicks in; DC 20 minimum for things that have pretty much everything stacked against the character".
Did...you actually
read the OP's posts, Paul? Because these house rules don't actually follow the math you're describing. Untrained skills suffer a -5 penalty--more or less equivalent to Disadvantage except that it stacks with Disadvantage--
and trained skills get +1/2 level. It's literally nothing like the standard 5e math anymore. By level 6, the gap between a low-stat (-2 or even -3, because they rolled their stats), no-proficiency (-5) character and a high-stat (+3 to +4), proficient (+3) character can be as large as -8 vs. +7--
fifteen points. Compared to the standard game gap of -1 vs. +5, or six points, it's two and a half times as much. And I'm not even sure that that's the whole story--I think there might be the
normal proficiency bonus on top of that, for a total gap *three* times as big as the "standard" game.
All of your comments here literally don't apply to the game the OP's DM is running. Not even in the least. Particularly because you're looking at proficient vs. unproficient, whereas he's looking at
Jack of All Trades vs. unproficient, and noticing that it's basically meaningless with his DM's houserules. Normally, at 2nd level, JoAT is giving +1 compared to a normal proficiency bonus of +2; with these house-rules, it still only gives +1, does nothing at all about the -5 penalty, and doesn't benefit from the +1/2 level thing.
[MENTION=6802927]Inoeex[/MENTION] -- I've just struck on an idea that, while it won't help you in the
short term, will help you a lot more in the
long term. Jack of All Trades specifically says that it adds half your Proficiency Bonus. Even with your DM's house rules, shouldn't that mean you should get half of the "half level" bonus too (or, essentially, one-quarter level bonus)? If the half-level thing applies to all skill checks as *part of* being Proficient, it seems like it *should* add to Jack of All Trades as well. Again, this won't get you much early on, but by level 8 it effectively doubles the benefit of Jack of All Trades. By level 12, you'll have a solid +5 to all non-proficient skills--eliminating the normal penalty. At maximum level, you'd have +8, or +3 after the non-proficient penalty is added in (compared to the normal +16, with no penalty).
A different alternative, if your DM thinks this excessive (which, unfortunately, sounds likely), could be to say "at 2nd level, and every 3 levels thereafter, decrease the penalty to skills you aren't proficient with by 1, to a minimum of 0." This means that, at 14th level, you make all skill checks at no penalty--you're still a full 7 points behind anybody that
is proficient, so it's not like you're going to become the Ultimate Skillmonkey because of it.
Another option, if you're on good terms with your DM, is to ask
why these changes were implemented. What purpose are they serving? How does your friend expect them to make the game a better, more enjoyable experience? If you can understand why they're being implemented, it may make you feel a little better about dealing with them. If you're looking for another example of a potentially dangerous rules-interaction, make sure to bring up Expertise, which both Rogues and Bards get--by doubling their proficiency bonus, in theory they should be getting +level to two (and later, four) trained skills--an utterly enormous bonus, given 5e's highly constrained number range. The only other concerning rules-interaction I can think of off the top of my head is Grapple: it's a special attack that uses Athletics (opposed by either Athletics or Acrobatics), rather than being an "attack roll" proper. With the massive disadvantage to untrained skills, and the massive boost to trained skills, a character trained in Athletics is essentially guaranteed to make--and maintain--a Grapple against a creature that isn't trained in at least one of those opposing skills. Since Grappling is a powerful way to control enemy monsters--especially when combined with Shoving--these rules make Grapple-using characters potentially broken.
And, finally, if nothing changes but you can't actually bring yourself to leave, you should also strongly consider picking up the Lore Bard subclass if, or when, you hit level 3. Lore Bard grants three additional skill proficiencies--on top of the standard 3 from Bard and 2 from background, that should give you a total of 8 (9, if you get a skill from your race) skill proficiencies. That's a massive number of skills--double what most characters get (2 from class, 2 from background). With 8 skills, you have nearly half of all skills covered--and since many are "doubles" (e.g. you don't really need
both Intimidate AND Persuasion, or Investigation AND Perception), you can cover an extremely broad array of skills with 8 choices. For example, since you mentioned (privately?) that you have low Strength, you could go Acrobatics, Arcana, Perception, Insight, Medicine, Persuasion, Stealth, and...perhaps Survival or Nature, for the grand total. Numerous background options could give you any two of those (and if you play an Elf, which gives you Perception for free, you could pick up, say, Deception instead), and your 3 Bard and 3 College of Lore choices are literally unlimited. Though you should remember that the 3 College of Lore choices would have to wait until 3rd level--try to put lower-priority choices, like Arcana, Survival, or Insight off until then, while prioritizing highly useful ones like Perception, Medicine, or Stealth.
You'll still get little to no benefit from Jack of All Trades, but at least you'll be crazy good (due to houserules) at almost half (or exactly half, if you get a racial skill) of the skills in the game!