Without the stats RPGs would just become another action game. The whole idea of an RPG is to have a character whose abillities might be entirely differant from your own. As it is I think we're seeing too much "twitch" in RPGs as it is right now with the way people bunny hop and circle strafe and such in things like WoW PVP (ie breaking line of sight before attacks go off) something which I don't think should really be a factor, and the actual problem that needs to be addressed with most PVP without going to a "turn based" format.
Generally speaking, RPGs are their own genere, if you don't care for the stats and such then you probably shouldn't be playing.
Also anyone who thinks the only thing that matters in a Paper and Pencil RPG is level has apparently not played many of them. If anything I think such a perception comes from MMOs that have implemented stats poorly, and where you really don't see much of a noticibale effect until the very highest levels.
To use AD&D2 for example, finding a way to finagle a natural strength of 19 allowed a character with such a stat to punch well above their weight class. A first level "Wild Elf Bladesinger" with a 19 strength could put out more damage than characters of vastly higher level with less muscle, and typically defeat characters several levels higher with ease unless they were similarly blessed.
Of course it's important to note that in a "true" RPG stats were determined randomly so the odds of getting such a character (unless the GM let you fudge the dice) were relatively nill. MMOs and to an increasing extent single player RPGs instead go with a set number of points on which to build your character as opposed to any kind of random numbers, meaning that everyone is equal and it all comes down to "builds". There are pros and cons to this, and like GURPS it leads to a lot of min-maxing and idealized point distribution.
I have often felt that MMO developers not only need to put more empathis on stats, but find some way of adding random elements to the entire process without alienating people who wind up with what they might see as "gimp" characters because the dice didn't land as perfectly for them compared to others.