[RPG] Does bounded accuracy effectively increase randomness in D&D 5e, compared to previous editions

Yes

This is, of course, intentional. One of the problems that D&D has always faced is that characters often have wildly different skill values, which can cause issues where some players get sidelined during skill-heavy sessions, because their characters don't have any of the right skills.

4e tried to rectify the problem of disparate skills in two ways: Skills were no longer based on Intelligence, and everyone got bonuses to every skill as they leveled up. 5e continues this trend: Players generally get the same(ish) number of skills, and the difference between skilled and not skilled isn't as large as it was in 3e.

The non-combat difference between level 1 and level 20 characters is not in how high their numbers are, but in their other capabilities. For example, a level 20 Rogue might not have an Athletics check that's that much higher than his level 1 counterpart, but his Second-story Work ability lets him climb much faster regardless. His Reliable Talent feature makes it so he never has a roll that's super bad. And his extra Expertise skills mean that even if he fails the Athletics roll, he probably has a high bonus in other skills that can help him finish his task anyway.

You are correct that the bounded accuracy rules mean that high level 5e characters aren't the invulnerable demigods that they were in previous editions. However, they are still versatile, powerful heroes that are still likely to (eventually) succeed at everything they do against a small number of low level characters.

Accuracy refers to the percentage chance that a given attack will hit. An attack may have high accuracy or low accuracy, but both of these are a measurement of accuracy.

Common usage also applies the word accuracy to include things that we don't normally think of as a "hit", such as a skill check, but it makes more sense if we remember that the DC of a roll is what's called its "target number", as per PHB p.7:

3. Compare the total to the target number. If the total equals or exceeds the target number, the ability check, attack roll or saving throw is a success. Otherwise, it's a failure. The DM is usually the one who determines target numbers and tells players whether their checks, attack rolls, or saving throws succeed or fail.

The target number for an ability check or saving throw is called Difficulty Class (DC). The target number for an attack roll is called an Armor Class (AC).

CTWind's answer cites an informative 2012 article which is the origin of the term "bounded accuracy", describing it initially in terms of attacks, then extending the concept orthogonally to other d20 rolls. Hence the reason why it's called "accuracy" even when it doesn't refer to attacks is that it's essentially the same mechanic as when it does refer to attacks.

In earlier editions of D&D, particularly third edition, numbers could get very high where high-level or highly-optimal characters with a lot of stacking bonuses were involved. A roll could be almost impossible for one character and almost guaranteed success for another.

Hence bounded accuracy, where the range of numbers it's possible for a character to roll is kept within tighter limits, or bounds. This shifts the focus of the game away from character optimization (by stacking small bonuses), and toward interacting with the fictional world by searching for in-situation ways to acquire Advantage.