There is this (false) concept called security by obscurity, and it sounds like what you're aiming for here. If someone knows what algorithm you're using, they could easily brute-force these keys. Protected anything of value with it, and you'll get rainbow tables of priv => public keys get published pretty quickly, meaning everyone already has a copy of all possible private/public keys. You can buy 2TB hard disks which have all the possible encryption keys for GSM - which is stronger than what you're suggesting here.
And perhaps you'd suggest keeping the algorithm secret. That doesn't work for crypto - everything about a strong cryptosystem can be known besides the private key in order for data to be secure.
Why even bother with cryptography if you don't care if the data is exposed?
One use case which I think would be valuable would be simply for teaching purposes. If you could find a public-private key pair just to illustrate the old "alice wants to talk to bob" scenario with very small numbers, that would help simpletons like me to understand the concepts better (perhaps).