I'm curious as to why you would want to remove one of the only mechanics representing progression and advancement?
First, who said I wanted to? I merely asked a hypothetical question. Regardless of whether I think it would be a good change or not, I probably wouldn't implement it simply because such a systemic change would require too much work on my part.
That said, for the following reasons:
1. Makes things simpler. No more updating every. single. number. on your character sheet at every even level. Also, keeps numbers smaller and easier to manage.
2. It doesn't add anything, and in fact subtracts. As far as I can tell, the only thing the half-level bonus does is make it so that PCs are restricted to fighting things in an admittedly generous level-band, and make certain enemies easier or more difficult based solely on the fact that they're not the same level as the PCs.
3. Keeps things consistent. Speaking as someone who falls squarely on the "extreme gamist" side of things, one thing I absolutely hate-hate-hate-hate is that (particularly mundane) challenges scale up to PCs, so that a level 1 PC might need to make a DC 10 acrobatics check to avoid slipping on some slime, while a level 30 PC would need to make a DC 25 acrobatics check to avoid slipping on some slime (which may or may not be masquerading as "Astral-Teflon Slime" to justify the DC increase).
This point bears repeating: You claim the PCs increase in abilities, but this is simply not true. That level 1 PC needs to roll a 10 or better to stay up, and the level 30 PC needs to roll a 10 or better to stay up.
That's my biggest pet peeve with 4th edition (and I'm still a huge fanboy of 4th, so don't get me wrong). I hate the way it looks like your character is advancing, but in actuality you still need the same rolls to beat the same obstacles. Granted, removing the half-level penalty won't help, but at least then the problem wouldn't be obscured.
As far as character advancement goes, it's still there. You gain hit points as you level, meaning you can stand up to more punishment. Your damage output increases as you level, meaning you can kill foes faster. Your tactical options increase, meaning that you can outmaneuver less experienced foes. You gain more feats, which you can use to increase your abilities, including gaining training or focus in skills, which is the only way for skills to actually advance in D&D 4th edition.
The only difference is, you don't have your numbers and your opponents' numbers inflating to make you feel better.