Very few features give any flat bonuses to hit in 5e, specifically for the reason you've pointed out. I would expect every character in the party other than a specialized archer to have +7 to hit at that level assuming no magic weapons, rather than the +9 you're using in the example. It may have been that your DM was throwing you up against lower AC creatures, causing you to hit more often, or you had magic items which break the bounded accuracy of the game.
You
are supposed to be able to fight lower-level creatures, which tend to have lower AC, though. That was one of the explicit design goals behind bounded accuracy, so you wouldn't ever need level 11 grunt orcs in your "Against the Orcs" campaign. And the game
should also be expected to accommodate magic items without breaking in half. If the game doesn't work when you include magical items, then they aren't really an option.
Monster AC, in general, seems to be out of line with the available tools for increasing your accuracy.
Bless is a second die which helps to normalize the probability distribution, and it's available at first level. Barbarians have advantage on all of their attacks, and can even hand it out to adjacent allies. Heaven forbid you use the "optional" rules for
flanking.
Honestly, it seems like the attack roll is more of a formality than anything else, and you can see this when you look at the HP inflation between the bandit (AC 12, HP 11) and the thug (AC 11, HP 32). The thug
knows you're going to hit it, but it doesn't
care because it can afford to get hit a few times, and
you may not be able to if you're fighting this CR 1/2 enemy while you're only level 1 or 2. (Incidentally, thugs also attack with advantage most of the time, even if you
aren't using the flanking rules.)
That's just the nature of 5E. Armor Class doesn't actually protect anyone, so Hit Points are the defining factor for how long you can stay in the fight. It's the main reason why some feats are considered overpowered. The math in 5E isn't quite as finely-tuned as it was in 4E (which should
not be held as the paragon of balanced math, given the amount of cheating they had to do in order to fit magic items into their system), but the system works
in spite of that since it uses HP as a giant slush factor, with trivial healing to keep PCs going indefinitely.