Spassky must have thought that this is one of whites best options. This was his standard reply to the petroff.

In the times of Capablanca the Petroff was a winning try for Black, so maybe he was happy to steer the game to an ending, and perhaps d3/Qe2 was best for his play.
 
That being said, this line is still a good winning try (for White) in OTB games for normal players. In super-GM games it is drawish because White can't make it complex enough to overcome their fellow 2700 technique, but this doesn't transpose to Opens. Here Black is usually weaker than White (as the Petroff contains a draw offer in the 3.d4 and Nxf7 line) so it makes sense for White to play an ending with many pieces. Perhaps somebody with a database will care to check the current performance and W/B Elo difference in the Qe2 line, e.g. by slides of 200 elo ? My guess is that White outperforms Black in the lower slides.

I also seem to remember that White need not exchange queens (e.g. with quick Be3/Be6, and also with some Qe2-Qd1 trick that was popular 10+ years ago). There's a big Petroff thread about an upcoming book in which authors will try to avoid the Nxf7 drawing line (presumably with the risky ...Bd6 instead of ...Nd7). If they succeed that would renew interest in the Petroff at all levels (other than just mimicing super-GMs and their special needs), but then, the book is not "Winning with the Petroff".