This is a matter of game-play preference. There are plenty of RPGs where your character only improves incrementally throughout their carreer. In Mutants & Masterminds, for example, you start with all your major powers, and as you gain experience you just gain some minor tricks and tweaks. (Many superhero games are like that.) GURPS Dungeon Fantasy is another example. You start as like a 250-point character or something, which is pretty buff, but then you only gain a few CP each session. In this sort of game, the plots and challenges you face remain largely similar throughout a campaign.
Personally, I LIKE the fact that D&D changes as levels advance. If the game didn't change, there would be no point to advancing. As a counter-example, remember the 3E Epic Level Handbook? I absolutely hated the bestiary in that book, because all the monsters were just bigger, but not any different, and that's super boring. It was a quantitative change but not a qualitative change.
I recently DMed a campaign from 1st level to 20th level (a first for me) over the course of a year (also a first) and I really loved how the game changed throughout the campaign. Session 1, the PCs were nobodies who happened to be in the wrong place at the wrong time. They struggled for survival and bigger people pushed them around. By mid-level, they were making a name for themselves, and setting up elaborate magical ambushes -- playing a very dangerous game. By the end of the campaign, they had literally taken over a country, ended a war, thwarted a plan to destroy the multiverse, and killed a demi-demi-god. They had all kinds of strange capabilities, and so did their enemies; killing major foes was no longer enough, because they might come back via any number of magical techniques. You can't have those kind of shenanigans if you stay at low levels. But if you start at high levels you miss the part where PCs are struggling for survival. In one of the campaign's earliest encounters, they fought enemies on a bridge over water, and it was scary because the water was murky and you couldn't see what was in it. In one of the campaign's very last encounters, they fought above a bottomless pit (it's a fantasy world; that can happen) and it wasn't a big deal, it was just kinda an obstacle that they had to plan around.
So for me, the radical changes across levels is definitely a feature. It's like D&D is multiple games in one. You could "fix" this by keeping the campaign within a tight level range. And you could also do the opposite with M&M or GURPS, by starting with low-point characters and giving out way more points per session than the guidelines, so your characters grow in power by leaps and bounds. But those games aren't exactly designed to work that way, so there may be some friction trying to adapt them to the different play-style.
