220V single phase to 380V three phase

[m_c]

It would likely still have worked with a 10k pot.
Even quick blow fuses, only trip fast if they see a big enough current. There are blow speed charts, which show that if only slightly above their rated current, they may take a few minutes to blow.
The big difference between quick blow and slow blow, is the slow blow allows for an immediate in rush of current without blowing. Over a longer period of time, they act similarly to quick blow.

Measuring the voltage wouldn't likely yield an accurate result with a standard multimeter, due to the switching nature of the VFD output (multimeters are typically designed to measure pure sine wave AC, and the high frequency switched quasi-AC output from a VFD can cause them to read high or low depending on the multimeter input filtering circuit).

If you were to switch to a servo, if you want to control the speed manually, then you'd need one with a drive capable of accepting a +/-10V input (most do, but some cheaper ones are digital input only, so best to get a manual for the drive to check), and some way of generating 0-10V (10V supply and pot, or 12V with an additional resistor in series so the Pot only gets 10V).
Or if you want to control it via software, you can just wire it to make use of step/dir (or CW/CCW or quadrature depending on your controller).
And to give an idea of the compactness, 400W and 600W servos can be had in 60mm, or 400W and 750W servos in 80mm frame size. The frame size being the overall size of the front mounting flange.

To give an idea of servo cost-

Lichuan A5 drive with choice of 200-600W 60 size servo - https://www.aliexpress.com/item/1005005440028771.html
Lichuan A4 drive with 400W 60 size servo - https://www.aliexpress.com/item/33049594917.html
Lichuan A4 drive with 400W 80 size servo - https://www.aliexpress.com/item/33050955694.html

The difference between the A4 and A5 drives (and motors), is the A4 uses an incremental motor encoder (outputs your classic AB quadrature), whereas the A5 uses an absolute (17bit) motor encoder. In terms of functional difference, there's not really anything notable.