What drives a poor reputation for the Rogue class?

[Psyren]

Also, it removes the ability for rogues to get sneak attack damage with reaction attacks (Battlemaster, Dissonant Whispers, OAs, etc.)

That change was reverted, rogues can SA once per turn again now.

I'm a 5e baby, did Rogues have that stuff previously?

I can't speak for 4e - but in 3.5, all Rogues could UMD, not just a single subclass, and getting your hands on magic items (especially consumables) to use it with was much easier / more readily assumed due to WBL being a baseline expectation. Moreover, their offense had a higher ceiling when optimized since sneak attack triggers on every hit rather than once per turn.

And for the bolded:

I just.. don't understand?

Between Uncanny Dodge and Evasion their defenses are pretty solid (and with mundane gear they're looking at a low-effort AC 17 top). They won't do it all day but they can fill in for frontline pretty well and can be built to do it even better.

What's not to understand? UD works on a single attack per round. By the time you have that 17 AC (8th level at the absolute earliest barring CL) most things you're fighting have multiple attacks. Being in the front also usually means plenty of Con and Str saves, e.g. things trying to poison you. They don't have shield proficiency and have d8 HD.

And with how Grapple/Shove works in 5e, Expertise lets them excel at it with really minimal investment.

It makes them not suck to be sure, but you're overselling Athletics Expertise. Most Rogues have a 10 Str if not 8, so your Expertise in Athletics still puts you behind a Str-based character with simple proficiency at most levels in an actual campaign. They catch up at around level 13, where most campaigns end. And even if you do all that, you're giving up your entire action to use it, compared to a Fighter or Barbarian or Paladin who isn't.

You could instead invest in Str + Athletics Expertise, but then you're making yourself a worse rogue to be better at something that someone else in the party can probably do more easily instead.