to do a random number collider would then need to also keep a database of each number tried to avoid re-trying..
(unlike a incrementor that just needs to store current position to avoid re-trying lower number again)
to store all these random attempts would require alot of space
00000000000000000000000000000000000000000000000000a14ed264b00000 =64 hex = 128bytes
00000000000000000000000000000000000000000000000000a14ed264b00000 = in hex = 45404136789770240 in decimal
so just to store 45404136789770240 attempts(if done randomly) would = 45404136789770240 *128byte
= 5811730terrabyte
now you should have some prospective of how many keys are possible if you start doing the math to then see how much data would be used up to log all keys tried
I think that if a completely random collision method is used, there is no need to save the private key generated each time, because the probability of generating the same private key twice is not high.
If duplicate private keys are indeed generated, it will not have a significant impact on the collision time and will not waste much time, as it is entirely a matter of luck.
It is more effective than the Large Bitcoin Collider mentioned above.