If Schoof's algorithm hadn't been discovered, Bitcoin would have just used different cryptography like RSA.
... or maybe it would use elliptic curves like RSA by users selecting a random group and using the hardness of finding its order for security. ... only to have it broken when Schoof's algorithm is discovered.

It is also very interesting that Satoshi used secp256
k1 and not the common secp256
r1, isn't it?