Stat increases can be a good thing if the rest of the system is built to be consistent with it. Two important questions are what exactly do the stats represent and how they affect tests during a game.
If we focus on the specific example of D&D, I agree that increasing stats is not a good idea. There are several reasons for it:
1. The advancement is already represented by other things (BAB and skill ranks in 3e, half level bonuses to everything in 4e). Increasing stats make it redundant.
Not in some ways. A higher state means, ultimately, a higher possible bonus. Without stat increass, such disparities are maintained indefinitely. That may be a preferable result, but it's definitely significant.
2. Each class has a narrow focus, making only 2 or 3 stats useful 99% of time. This encourages increasing high stats and ignoring low ones, making the spread greater with all problems that come from it.
I can't speak with authority on 4e, although I recall that mechanics make it possible to have two or three dump stats. In my 3e/Pathfinder game, this philosophy will get you killed. Perhaps it's a playstyle issue, but virtually every game of mine involves something like perception checks, grappling, a variety of saving throw attaks, and so forth. You can probably get away with dumping your two least favorite abilitys cores, maybe.
3. While high stats are harder to get at character creation, the difficulty of increasing them in game does not depend on stat value. It leads to the same issue as point 2.
That is something of an issue in that it's true the price doesn't go up, leading to min-maxing. However, the optimal spread is usually to spread your stats, rather than paying a premium on very high abilities in the beginning. Also, the relative disparty, if it continues, should remain about the same within a given class. That is, Int 18 wizard and Int 14 wizard remain even if they both focus on Intelligence. So, in summary, it shouldn't lead to the same issues as #2 unless the players decide to focus on a very specific style of optimization (one that in I feel in 3e does not pay off very well).
4. Nearly nothing depends on the stats alone. Because of that, the stats by themselves have no meaning. It's impossible to tell what given value of a stat represents, because in-game events would contradict it. That's an argument for removing stats completely, not only for not increasing them.
AC bonus, damage rolls, ability checks. I really feel like a 12th level rogue ought to have a better AC and Dex-based ability checks.