The steep power and complexity curve in D&D (5E, yes, but also 3.x and PF) expressed through it's leveling system is a bug. it makes the game less fun for me, particularly as a GM. it breaks my sense of immersion in the world and it limits and constricts the kinds of adventures, campaigns and stories that I can tell through D&D. D&D would be better if leveling were divorced from the power and complexity curve.
Discuss.
You are in the minority among D&D players, as this is not a bug, but a core feature of the game. Any RPG that uses levels is going to have the issues you describe, but oddly 5E is probably the one with the least issue for you (except maybe OD&D, but unlikely).
In AD&D and BECMI, characters may not have gotten as many features/complexity as they leveled (as opposed to modern gaming principles, where every level is supposed to matter), but they DID get a lot more powerful (especially casters). 3E upped the ante with the attack and save bonuses (not to mention skills), and added in additional complexity of prestige classes and feats. 4E was both better and worse, for while it could allow you to easily reskin monsters to be the same type (such as a campaign against an orc nation) to use at every level, the characters were on a treadmill of constantly gaining more and more power and abilities to be used against more and more powerful enemies.
5E is different. While characters still get more powerful/complex, they do so in more limited ways. A 20 ft wall is a significant obstacle at level 1, but even at level 20, unless the character has a specific ability (proficiency, class ability, or spell), it's just as difficult to overcome, since the check is exactly the same. Weaker enemies remain viable much longer, simply by adding to their numbers, allowing a more LotR type effect. Yes, eventually orcs will have to be phased out if you continue the campaign long enough, but something that many forget, is that most campaigns end around level 10. The leveling complexity increases dramatically past this point, requiring a more epic story.
You have mentioned that you are not looking for a fix, as you already know how you could fix it. Something to consider is that D&D (any edition) is not the right game for you. There many other RPGs that are more story based that can provide a much better example of what you like (I'm a huge fan of the original Deadlands RPG myself). Most of them use skill/ability points for character progression, which can be slow or quick, depending on the GM and system. 5E was playtested to appeal to the broadest possible player base, but this means there are still going to be people that it is not a good game for.