I fully agree that playing thousands of bullet games just with the rating in mind (as many do) is a waste of time. But as a time-trouble addict, around the same time I started playing a lot of bullet my focus in those stressful otb time troubles (and my results) improved. I personally think there was a connection. After a year or so I realised that bullet was not helping me improve anymore, and I cut down on it, happy with the training effect I had achieved.
About blitz and bullet not giving you time to think and plan:
This is of course true, but to my mind this is exactly what makes it valuable as a training tool! After all a big part of playing strength comes from absorbed and unconsciously recognized patterns ("chunks" in the scientific terminology), which then form the
starting point for planning and calculation. By storing and analyzing one's blitz games, noting when mistakes occured and the position worsened, one can get some insight into which patterns are lacking and should be "strengthened". As an example, I noticed that in blitz games I repeatedly made the error of underestimating the value of an active king in the endgame, even as compensation for material. This is very useful information for finding training exercises! Similarly, one can pinpoint tactical errors that recur, and discover that one should work on for example "the overworked piece" or "the weakness of the back rank" or whatever. Finally blitz is useful for quickly gaining experience with an opening one is learing.
Of course, all this presupposes a) that one is conscious of blitz/bullet being used for a purpose, not for its own sake, and b) that blitz should never be the only kind of training (or play) one engages in.
Edit: I suppose the debate of blitz
versus bullet as time-trouble-training depends on just how extreme one's time troubles are. I for one am not unfamiliar with having to make 10-15 moves in a minute, when focus, swift reaction and avoiding blunders is everything, so bullet made sense