Sure, ARAM exists - but like I said there's an always-changing array of free champions, so it's not like you'll never get them. And again - if you're just starting out, there's going to be some time before you even get around to trying every champion for the first time. Even if you go with ~30 minutes per game(below the average length in normal modes, slightly above average on ARAM) - you're looking at upwards of 60 hours of playtime just to try everyone once.
You can complain about F2P games all you like, but I don't think for a second we'd have had as many new champions released if they'd been on a pay-once model. I don't think that's exploitative, just different.
-edit- before my play patterns are criticised again, I should say I've been playing LoL to varying degrees of intensity for about 5 years. I think it's more accessible in terms of champion acquisition now than it was then.