Well it’s not that 16 is awful on its own. It’s awful when there aren’t any mechanisms to get out of melee without catching attacks of opportunity, and your kit wants you to be in melee. Also you: This is still sub-par AC for anyone going into melee, especially without an on-turn disengage or shove)

16 AC is not, and I quote, "Sub-Par" as long as you are not trying to take on a tank role within your party. It's perfectly fair for anyone who might be stuck in melee.

That being said, if you enjoy the benefit of using the UA version of tavern brawler, go ahead. Just keep in mind that that version of the feat may not make it into the print revision of the PHB.

and you're acting like 16 AC is "F" tier. If 18 is "S", then 16, the next possible starting value, should be A. And that is more than "not decent"

18 AC is only 10% less likely to be hit than 16 AC, and not every character will use a shield - in fact, most don't. So now I know your understanding of the mechanics behind the game is inherently flawed.

Unfortunately Mage Armor would overwrite the unarmored defense feature. Shield is the only thing that makes this class possibly have decent AC, but I am hoping and praying that it gets the nerf-stick in an upcoming UA.

Agreed, Mage armor wouldn't allow you to benefit from Charisma to your AC, so it wouldn't be a massive benefit. However, given how little effort it takes to start with an AC16 (16 Dex, 16 Cha, 14 Con is easily doable at level 1), to call it anything less than decent is insulting. I guess Paladins and Fighters don't have a decent AC either, since the chain mail they can start with has an AC of 16. Plus, a Dancer can easily hit AC 20, with no gold investment (plus has access to Shield and Absorb Elements, making their resilience even better) - tying them with Heavy armor + shield usage.

The dance Bard has to get into melee range, then wait for another creature to have its full turn to do all the offensive things it wants to do, before ending its turn next to an ally, then they can move away.

That's part of the clunkiness. If it acted like the scout rogue's ability, and triggered as soon as an enemy ended their movement next to you (or an any ally), and not end of turn next to an ally, it would be a better ability. However, the claim was that Dancer has no means to get out of melee unattacked - this is not the case. Inspiring Movement lets them do that, it's just bad at it.

This doesn’t actually get YOU out of danger tho

It does. Enemy moves next to ally, you can move away and your ally can move too. It's clunky in that you can't trigger it, and it requires the enemy to target your ally over you, but it works. (And I disagree it's wanting you to swap with your ally - the movement limitation and the range on it make it very clear that is not the case. If it was meant for you to move up to 60ft, you'd not have your movement halved - it's more meant to let your party rearrange and deny enemy attacks more than anything. The free parting shot is just that, a nice bonus rider)

Yes, Charisma + Dex armor is neat, but since Shield + Light Armor would get you to the same level of AC, it isn’t an upgrade over the baseline Bard starting out. (For some reason I thought Bards got shield proficiency. This is still sub-par AC for anyone going into melee, especially without an on-turn disengage or shove) Later on when you can max out your Dex and Charisma to 20, it would be eventually higher AC, but full casters typically don’t want to put a lot of investment outside of their casting stat.

And casters typically don't have a lot to spend their stats on outside of their casting stat. Making their armor lean into them being more MAD is a good thing, since bards usually have the ASI's to spare. Starting with AC 16, spiking to 18 by level 8 is still decent with a 16/16/14 Dex/Cha/Con spread, which is doable at level 1.

Almost every Monk subclass has some way to avoid getting hit while darting in and out of combat3

And so does the Dance Bard. Inspiring Movement does not trigger attacks of opportunity, so if an enemy ends next to one of your ally, you can move up to 15ft (halve movement) away from nearby opponents without getting attack. Your ally can then move up to 60ft (regardless of their own movement limitations) in response. It's a bit clunky, but something that you can trigger relatively regularly.

2 And note that Bardic Inspiration is tied to your Charisma modifier. So as resource hungry as the Monk is, this is worse.

Level 5 - Bard can spend their spell slots to use Bardic Inspiration once per turn. This means a bard can get up 2 back per round from Font. (burn a spell slot on your turn to use a bardic inspiration, then on another player or opponent's turn, burn another to gain a new one once you have used your prior).