Short-term peak ratings for electric motors are always huge. You can put in higher voltages up to arc-over. More interesting is sustained output. 1 minute, 10 minutes, 1 hour, continuous duty. That's all about how well it can get rid of heat.
That's why electric motors have a "temperature rise" number on the data plate. That's the steady-state temperature increase from a cold start when run continuously at rated power.
edit: After looking at your account, I see you are John Nagle, and I worry that I am confidently-incorrect here, lol. I'll leave the comment as-is because it is still my genuine belief, but feel free to correct me if I'm totally off!
A big problem with older permanent magnet motors was that too much current could produce a field strong enough to demagnetize the magnets. Supposedly this is is less of an issue in the cobalt-neodymium magnet era, because the coercivity of those alloys is so high.
Then there's finding a pulsed current source to power the windings. Ultracapacitors are good for that.
Then there's finding big enough semiconductors to switch the thing. This, too, has become much easier. It's amazing how much current you can put through modern power MOSFETs.
Then there are mechanical limitations. At some point, something is going to bend from sheer torque. At some point below that, the windings will distort a little on each cycle and wear out.
Applications for this include railguns, catapults, and electrically launched rollercoasters. Interestingly, they're all linear motors.
(I haven't looked at this since the 1990s. The components needed are now far better and more available. Mostly as a spinoff of the electric car industry.)
Cars are a good example of this. There are very few public roads in the world where a car can use 1000hp for more than a few or perhaps a few tests of seconds at a time. On a drag strip a 1000hp street car might run a low 9 second quarter mile reaching around 150mph. That'll put you in jail if a cop sees you doing that speed in a lot pf places. To maintain the fastest speed limit in most countries probably doesn't even require 100hp. So a "short term peak rating" that lets you use 1000hp for 10 seconds will accelerate you in a _very_ "sporting" fashion for as long as you're likely to be able to hold the accelerator down (outside of a race track or autobahn).
Back when I raced quadcopters, I'd happily set them up to pull 200% or more of the rated power of the motors and batteries, because if you kept it pinned at full throttle it would have vanished out of sight within 2 seconds. (You had to be somewhat more circumspect with the motor controllers, the magic smoke could come out of those way faster - sometimes going pop effectively instantly if you started to approach 150% of rated capacity, sometimes even 120% would blow them up ij just a few hundred milliseconds.)