The fact that you can continue to increase the factor by which you avoid being hit, to unreasonable levels just sits wrong with me. I don't care how magical your armor is, or how good you are at fighting/dodging, at the end of the day even a zero level scrub should be able to hit you. Now, taking damage? that should be a different story. [...] But then I have a problem with the stat increases as well, so maybe I should just go back to playing BG1/BG2 and leave it alone.
It sounds like you got burned by the inflation problem that 3rd edition had (and which pathfinder inherited from it) - where numbers just kept growing and growing ridiculously, and you'd end up with wizards with AC 50, and characters making skill checks against DCs of 90, and anyone who wasn't super-specialised to do a particular thing couldn't even try because there was no possibility of success unless you were specialised...
Fortunately, more recent versions of the system alleviated that problem.
In 5e, we have bounded accuracy as a principle that generally restricts the number bloat and means that specialists will have an easier and even a near-certain chance of doing the thing they're good at, but that most characters will generally still have a chance to succeed. AC generally doesn't go above ~23, at any point of play, or lower than ~9. Attack bonuses start at ~+2 and rarely go above ~+12. Ability scores for players start around ~10, but rarely, if ever, go above 20 (they can't without specific magic or abilities). Monster's Ability Scores can go as high as 30, but no higher.
No matter how good you are, a basic scrub still has a chance to land a lucky blow, and deal damage; you always have a chance of scoring a wound on that dragon - but the hero with experience, and magical gear has a much better chance and will almost certainly hit more regularly.
