No. That appears not be the situation. Immunity shortly after the thirds shot is substantially higher than shortly after the second
YMMV. The UK gave out AZ and Pfizer. First at a 12 week interval, then shortened to 8 weeks.
The question is: too quickly for what? My understanding is that
a) If the goal was optimal immunity in the longer term then yes, it might be overly quick.
b) But if the goal was fighting the raging pandemic that needed urgent actions right now as "the house is on fire", and you have a lot of vaccine doses, then no, maybe not too fast.
Finally, a lot of vaccine courses require more than 2 doses, separated by more than a couple of months. UK standard childhood vaccination schedule for instance. "Polio" is in there 5 times. Polio is a memory, but only because because to this day they don't mess around with vaccinating against it
There is a reason for that - what's being deployed is what has been tested. You could work out an optimal schedule, but that might take years of trials, and meanwhile people are dying.