That’s how I roll with it. You already own that old motor and unless your down time cost is extreme, you might as well use it and replace it with a better one when it fails.
Given the supply chain issues right now though, I would suggest ordering that replacement and keeping it on the shelf.
The anecdotes on old motors surviving for years has some problems though.
First off, if discussing 230V or less, that’s one reason. The voltage stresses created by VFD use at 230V are usually still way below the insulation level used on the motor windings, ESPECIALLY if it was a 230/460V motor.
Second, older VFDs used even 15years ago had a different type of transistor system that operated at a much lower switching speed, so they were less inclined to cause these voltage spikes unless the distances were long, as in over 100ft from drive to motor. So it was entirety possible to “have a whole plant full of old motors on VFDs” and never see a lot of motor failures. But modern VFDs that are designed to be smaller/cheaper/faster use transistors that switch on and off 100 times faster than the older generations, and it is the steep rise time of the pulses that helps to make this problem worse with shorter lead lengths now. So people often pull out a 20 year old VFD and replace it with a new one, then the motor fails within weeks.