This seems like at least something of a bad idea, because that implementation (if my search-fu is correct) is:
https://github.com/torvalds/linux/blob/master/crypto/aes_gen...
Which is obviously not constant time, and will leak information through cache/timing sidechannels.
AES lends itself to a table based implementation which is simple, fairly fast, and-- unfortunately-- not secure if sidechannels matter. Fortunately, AES-NI eliminated most of the motivation for using such implementations on a vast collection of popular desktop hardware which has had AES-NI for quite a few years now.
For the sake of also being constructive, here is a constant time implementation in naive C for both AES encryption and decryption (the latter being somewhat hard to find, because stream modes only use the former):
https://github.com/bitcoin-core/ctaes
(sadly, being single-block-at-a-time and constant time without hardware acceleration has a significant performance cost! ... better could be done for XTS mode, as the above algorithm could run SIMD using SSE2-- it isn't implemented in that implementation because the intended use was CBC mode which can't be parallelized like that)
Can't the kernel aes-ni just be setup to save the fpu registers itself on the stack, if necessary?