I used to think this and still do to some degree but, in all honesty, whilst the game does not truly "begin" at level 80, a lot more possibilities open up at 80. So I agree and I disagree.

This is why I believe the game can "begin" at 80: Quests I haven't done I can still do at 80, I can choose to solo content and old raids for a "challenge" (and I do), I can PVP at a ranking which is the most balanced, I can do Arenas and much more Battlegrounds, I can raid and do Heroic Dungeons and get the best of the best gear, I can actually "help" in events like the upcoming Gnomeregan and Echo Isle events and actually feel like I done something, as well as other things.

This is why I don't: I enjoy levelling myself, not for the quests or for the exploration but mostly because it's always there. I am a massive altoholic, I have a lot of alts at all varying levels for when I get bored of one character. I have friends I enjoy levelling up with who have alts as well, exploration WILL become one of the reasons come Cataclysm and sometimes I regret levelling certain alts before the expansion (but oh well, I'll do it again anyway, lol).

Levelling is also a reward in and of itself. I enjoy levelling up and I enjoy getting new gear because this is what "progressing" feels like to me. I play the game a lot but I am by no means a "hardcore" raider. I have my main that raids but he is not as geared as many others on my realm. This is for a number of reasons and to compensate for that I level up, it's just my cheap way of feeling like I've accomplished something, in a sense. Some of the more mundane achievements are also nice (like rep grinds or The Insane). It also requires ABSOLUTELY NOTHING to begin. Gold and easy bags from my mains makes it easier but aren't necessary, heirlooms are nice but again, are not necessary.

Being level 80 is fun but depending on your playstyle or how often you play, you can't do all the things that level 80 has to offer. Levelling and alts can be a good substitute for this. I believe many things start at 80, but not the entire game. I think it's extremely ignorant to state that as well and, if you think that, then as Cetha said, you're selling the game short.

Remember folks, this game has A LOT of stories to tell from 1 to 80. Ever tried reading that quest text every once in a while? Some of it's pretty interesting.