de-spidering a cheap driver?

What do you think would happen if you removed the spider from a small 2-3" full range driver?

Would the voice coil just stray off center and ruin it?
These kind of small and shallows FRs are sort of close structurally to being cone tweeters already so I think there is some chance it could work.
Whether it would work well and actually benefit something is another question.

I was thinking about this into a relation to using a cheap small FR (CHN40, P830985, Faital 3fe25) as mid tweeter in 2 way, and making into poor mans Alpair 5.3.
 
Removing it completely might be risky.
My first speaker build was off a Danish design using SEAS 6.5" drivers and one trick was cutting 'pizza slices' off the spider all around. Leaving about half the spider but in 6 smaller pieces. This held the voice coil centered but loosened up the driver for what ever reason. I had those for about 10years without any issues. (I never tried with and without this mod, since I followed the design instructions, so have no idea regarding the effects of doing this)
 
FWIW, Hornresp can simulate what will happen at low frequencies when you increase the suspension compliance.

IIRC, the cabinet air-spring dominates the driver's suspension in smaller enclosures, so the change in driver compliance has minimal effect. If the cabinets get large, though, things would likely be different.

Chris