Lawbag, you're mixing up point-buy and non-level-based and I think that's getting you some answers that may not be as useful as they could be.
It sounds like your player really just doesn't like class-based (and possibly level-based) games. This can cause problems with your spec since you write
low power gaming system, not suited for high or epic gaming
and really, most non-class-based systems, which are also usually non-level-based, tend not to work well for epic gaming. The reason: fundamentally, without levels, you tend not to get escalating hit points as characters improve. They just get better defensive skills, and it only takes one botched parry/dodge to kill a character.
So I think you probably need either a system that still uses levels and escalating hit points, but which (at least) strongly blurs the concept of "class", not to mention doing away with random chargen, or you need a system that just makes it very hard for PCs to die in the first place.
Off the top of my head, I'd suggest Talislanta 3e for the first option. A side benefit is that it's now free and there are a fair number of adventures for Tal. (Note: Tal is pretty nonstandard fantasy. Not sure if that's a selling point for you.) For the second option, you might look at d6 Fantasy, which I believe is also free now. I don't know d6 very well, but after reading a bit of the original Star Wars rules, it sounds like characters are pretty hard to kill.
Of course a cheap method of making any character hard to kill, and even giving them additional "staying power" as they advance, is to use "hero points".
If you really want to do away entirely with levels and random chargen, then Talislanta 4e might be up your alley. Also free. For a similar system and more traditional fantasy, then Atlantis: The Second Age or High Medieval might be options.
If you want to get rid of random chargen, but you can get away with just sort-of blurring the rigidness of classes & levels, then Fantasy Craft might be an option. It's not for me--too fiddly and too much d20 still in its bones--but it might be for you. I have a copy for sale by the way.
BTW, have you asked the player what systems he/she does like? That might give us a better idea of what to suggest.