I would be stalemating every time playing that fast as well. Very difficult to learn from mistakes and the checkmate patterns playing fast time controls which is why I stick to 3+ days a move. Bullet games are good to watch but it's more about avoiding blunders and not losing on time than strategic thinking and creating brilliance (some tournaments have brilliancy prizes and I think that lad from The Fast Show presents them on behalf of FIDE)
Brilliance in a bullet game would be equally if not more impressive than a classical game. I'm not sure what the stats are with brilliance ratios across the time controls.