I don't think the minutes was a huge issue with GS in the regular season as they were able to rest most of their key players late in games due to blowouts. But I think going for the record put a strain on the team as a whole. Even Kerr said near the end of the year that it was taking a toll on them mentally. They had a ton of media coverage and a ton of pressure.
And no one can knock them for going for the record. If we had the Sonics, they would have done the same. If the Seahawks are 12-0, I'd expect them to go for 16-0. While it is cool and everything to have a regular season record, in the grand scheme of things, it usually means little to nothing. In general, people tend to remember champions, individual records and then team records. Lets be honest, I could care less that the Mariners won 116 games in 2001, mainly because we got embarrassed in the playoffs.
It's a mix of GS hitting a wall and OKC peaking at the right time. OKC kind of slept-walked through the regular season and have finally put things together. I have OKC winning tonight, GS in a blowout in game 5, and I think game 6 will pretty much be the deciding game.