Smarter people than I have written on the failure of growth in conflict resolution ability in games such as Dungeons and Dragons. Here is another article, talking about the linear nature of the d20 check. Here is an article with lots of interesting statistics!
This post covers two topics:
There are a large number of issues with the d20 as a resolution mechanic for conflict resolution.
Topic one, the d20 as a resolution mechanic. Pathfinder example:
"I'm going to arm wrestle the ogre!"
"What's your strength modifier?"
"I have a strength of 8, which is a -1 modifier!"
"Ok, roll a d20, while I roll for the ogre who has a strength of 21 for a modifier of +5."
"I rolled an eight!"
The DM looks down at his 1 and wonders how the world went wrong.
Ok, so here's the simple math - the noodle armed wizard will beat the ogre in a strength contest of arm wrestling 22.8% of the time and tie 3.5% of the time.
[Edit: Someone pointed out these numbers are wrong - I apparently forgot to calculate the 0 value for the difference between the skills. The actual percentages are 19.5% the person seven ranks lower then his contested opponent will still lose. Apparently ties (even though they are mathematical ties) always go towards the person with the higher total in 3.5/pathfinder? Either way, in any contested roll, If I have 7 ranks more than you, I still lose a full 1/5th of the time. Pick whatever contested roll you wish. Notice the underlined point below.]
One quarter of the time the ogre will not win in an arm-wrestling contest. [Edit: one-fifth of the time]
The d20 has no mode value. Given enough rolls the average result (mean) will be 10.5, but on any given roll the chance of receiving any result will be equal to the chance of receiving any other result.
This is such a large and known problem, that the game explicitly acknowledges it and includes a rule for bypassing the roll completely (take 10).
This can be an advantage for something like combat, where highly variable results can be extremely exciting and entertaining. It is chaotic, and huge swings in luck are expected. The high degree of randomness in combat is a large benefit for creating a very real threat and fear of engaging an enemy, leading to interesting role-play to avoid combat and exciting comebacks against overwhelming odds. But for resolution of activities where increased accuracy is expected with increased ability it fails totally.
There are a large number of issues with characters having the ability to increase their skills used for conflict resolution.
Topic two, the scaling mechanic.
Here's another example with level 15 players.
"The bridge is liquid, shifting before you. Heavy winds buffet the path. It's a dc35 skill check to cross!"
"Sweet! I've got a (+9 stat, +15 ranks, +3 class, +10 magic item) 37 in my athletics!"
"Damn! I've got a (+3 stat, +0 ranks) 3 ranks - I can't make it even with a 20!"
Again, simple math. Escalating DC's and increased specialization create situations where characters can be whole statistical probabilities ranges away from the next tier of a successful roll, while other characters can have auto successes. The degree of specialization afforded high level characters easily breaks the game. (and the above 37 rank PC is not one that is even particularly specialized in athletics, just what you would expect a reasonably designed 15th level rogue to have)
This is an artifact of the range of results on the d20 being low compared with the range of possible skill modifiers. This issue intersects with an issue with 'skill tax' skills such as concentration (eliminated in pathfinder) and perception. Someone always keeps these skills maxed, questioning the advantage of 'increases at level'.
These are known problems, and there are a large number of suggestions and house rules created to address them.
So, what advantage is gained by having skills that increase with level increase, given the problems they cause above?
and what advantage is gained by having a mechanic for something as chaotic and random as combat be used for something that expects a more consistent result?
[edit: removed the word 'universal' in front of mechanic, since if the mechanic were universal it would be used for skills, natch.]