The only game I've ever felt did F2P nigh-perfectly was Blacklight: Retribution, and that was because of the ability to rent weapons and upgrades, in addition to buying either of them all out. Renting is something all F2P games should incorporate, because it allows you to both try weapons and weapon combos, sink extra points into weapon you like but can't afford to make permanent yet, and stay on par with people who simply went out and bought everything.
In PS2, I finally earned a total of 1000 Certs after about 50 hours of play - Including messing around, AFK'ing and such. Now, if I hadn't purchased a single item during those 50 hours, I could have gotten one of those really expensive weapons... Only to discover that it didn't fit my play style. (Note, this is purely theoretical. I did buy a bunch of stuff between then and now, and I don't regret any of it.) With a rental system, the problem of spending 50 hours of game time to earn a single weapon you end up disliking is a poor choice rather than a design flaw. Heck, with good rental deals I'd accept seeing 2000 cert weapons, and you know I'd work towards making my favorite weapons and upgrades permanent.
PS2 certainly isn't P2W, but folk who pay are pretty far ahead in the arms race compared to free people, simply because freeloaders like me can't earn the equipment they want to stay competitive (Or at least feel like it).
It doesn't help that the game totes everything as a "side grade", yet requires you to play the game as a full time job in order to get weapons that are, in theory, on level with other weapons.