I agree that I'd actually like to see Tristana's abilities without AP scaling either - I think it's perfectly acceptable for champions to have non-scaling abilities because it forces you to think about early vs. late game strength. I like the existence of scaling abilities, but I think that maybe Riot are too invested in them because that's one of the biggest differences between LoL and the traditional DotA model.
I think you're right that a game needs to be intuitive, but I think that remit only extends so far. Looking at it from another perspective, a game needs to involve intelligent decisions - especially if it's designed for competitive PvP - that allow a smart player to optimise their play and get one over on their opponents.
I think you're overestimating the role that the designers should play in determining how the game is played. The designers provide the raw materials in the form of mechanics, champions and items, but it's actually the players that determine how the game is played. Kennen has quite a clear focus on ability power in terms of his design, but I don't think some top teams using him as an AD carry means his design is inadequate - it means players are being inventive with what they've been given. Kog'maw is almost always played AD at a high level, but he's my favourite mid AP because I decided it works very well for my playstyle, and I wouldn't like that taken away because every champion needs to have exactly one obvious build type.
I don't think it's possible to make LoL easy for new players to understand, but then they don't actually need that understanding if they're playing against other new players. Sion looks like a good AD champion to new players because he's actually a pretty good AD champion for new players - In games of around level 15 or below, I saw AD Sion a bunch of times and it worked out pretty well, because as a new guy the only people you need to be on a par with are other new guys. People learn about champions and roles organically - I don't think design should be too restricted by the way a brand new player will interpret it.