All the champions so far in League cost 504,300 IP combined.
Playing on a new account and realizing how much I'd have to play to unlock even a quarter of the roster again (the majority of champions are in the upper tiers of IP pricing) is just a tad discouraging, and that's without considering runes.
I don't have any particular champs or roles I'm good at, either, so I can't even prioritize any champs over others to buy.
A FWotD is, we'll say ~240 IP.
Assuming you get Garen/Trist/Ali for free, that leaves 501,150 IP to get the remainder of the champions.
That's close to 2100 first wins of the day to buy all the champions. That's like 5 years' worth of first wins.
Of course, you'd ideally play more than just first win games, so that's just conjecture. It's still pretty silly to think about, though.
The grind is real.