Interesting notion. I think there's an argument to made that the Telecaster is, perhaps, more workmanlike that the Strat, but I don't think that makes it any the lesser. Indeed, to my mind there's something much classier about something that is simpler, more refined, that somehow makes it feel more expensive. Where perhaps the budget angle comes in is that if you're wanting to sell a Tele type and a Strat type for the same money, particularly at the lower end of the price scale, the money goes further when the design is simpler - two pups not three, no trem, that sort of thing.
FWIW, much as I feel there's a place for everything on their scale and that Fender do it perhaps better than anyone else in terms of multiple price-points, I often think of Squier as the closest thing to what Leo had in mind originally: giggable, easy to repair and upgrade, at a very affordable price.... I've owned Fenders from the MIA, CIJ and Squier ranges; love them all. Currently eying the tidepool Strat in the Player series....
Back to the SG, though, I totally agree it's a lovely thing - if anything, I appreciate its simplicity as classier than a fancy top LP. If I were buying an SG, I'd definitely be looking to Gibson, whereas for an LP type I tend to feel the money is better spent elsewhere these days. And yes, an SG can do anything an LP can do.... though that's probably rather more in Clapton's hands than in mine.