I'm a big fan of stats, but I never really liked what came out of it in TES. I'm against their removal in Skyrim, but honestly I actually think it plays out surprisingly good without them. The biggest challenge in stats is making them useful yet balanced over the leap of lots of levels - everyone says it has to progress (unlike in Fallout where they are static), and everyone is obsessed about maxing and no caps, complete with additive stacking of effects.
These demands ruins much of the potentially good effects that stats can have. They either feel useless to the role player, or they become over powered to the power player. Take i.e. speed in Oblivion. Max it out and add a ton of additive bonuses to it, and you could probably reach 300, making it appear utterly ridiculous. In Skyrim, your speed is static, but it's set at a fairly high pace (games do that usually), and it actually feels pretty good with the way sprinting works as it doesn't give you a get out of jail free card anymore. Keep in mind, a living thinking GM does know how to get around power players - a generic game algorithm generally can't.
I only see a few possibilities around stats:
1) Pretty much locked at low levels (Fallout), where you don't get to change things very much. This counters the idea of evolving throughout the levels, but does allow for some nice checking that FO/FONV already utilizes.
2) Put you stats in the 30-70 range with a 50 average, where you increase one selected stat every level. Obviously there will be no maxing out everything, and it's governing only as a percentage of your skill.
3) Counterstats, where instead of always evolving something it now comes with the cost of decreasing a counter stat. Works in pairs, i.e. Strength/Stamina, Intelligence/Willpower, Speed/Dexterity. Problem with this one is that it is hard to design around. When you introduce a new idea to the system, the balance is disturbed unless you also design an idea to follow up on the counterstat (with fairly equal user usability/desirability).
Another problem is that no matter how deep you make the stat system, it alone won't do the appropriate effects to the system unless you start hooking up external tables. This gets away from generalizing (which helps automation during the implementation phase) which tends to be most developers primary goal (for good reasons of course, even if we players tend to hate it

). An example of this is the ability to jump.
* Is it governed by skill (acrobatics) how high you can jump? Yes.
* Is that skill (strength or stamina or endurance or willpower? makes you think!) governed by stats? Yes.
* Are there external (what are you wearing? how much weight do you carry?) influences? Yes. It suddenly grows very complex, for a single ability.
Bottom line: Stats would be great, but it actually needs to be a lot deeper to have good impact that makes sense. But this sort of complexity in a "generalized system" is something developers try to avoid, for very good reasons.