I think the impedance mismatch alone may be a problem, causing either the push or pull side to have a different load. Even with the same bias load, the frequency response can also be different enough, to possibly overheat the output transformers. I've used two different brands in each side (same number), for a blend that I liked better. This was as much of a difference I have tried. But, I wouldn't risk a totally different tube in each push-pull side.
Tube mixing
So what would happen (theoretically anyway) if in a "push pull" tube amp where each tube has its own bias pot, you stuck disparate tubes next to each other. I have 3 sets of power tubes...if I put 6550s and KT120s next to each other in each channel biased properly (or to the amp specs), or a KT88 next to a 6550 in 1-2-1-2 pairs...would this trigger cosmic calamity? Gear meltdown? Audio magazine subscription rejections? Would the tubes sit there and stare at each other in disgust? I'm not necessarily gonna try this, but it seems to be a way to get the advantages of different tubes ALL AT ONCE! Ha...and hmmmmmm....