You will not be able to have all the private keys since most of the keys are private, and the mentioned services are just for spamming with viruses.
It's perfectly possible to generate a private key that was previously generated by somebody else. Case in point: brainwallets... There once was a website that would allow you to generate a private key that was directly derived from a passphrase you entered. After a while, a white hat hacker proved that, using a simple dictionary attack, he was able to generate a lot of "existing" private keys, whose public key hash (addresses) were still funded with unspent outputs.
I think the problem here is that people's minds are just not capable of understanding big numbers. Eventough the keyspace is not infinite, it is sooooo big in reality it's impossible to actually generate and scan the complete keyspace. People see numbers like 2256 private keys that result in 2160 addresses and think "hey, that's a number i can actually read, so there must be a program that quickly loops trough those keys and prints the ones whose public key hash is still funded". In reality, however, 2256 is a number sooooo big, that this task is simply not possible.
All sites like keys.lol are practical jokes. If you read the code pooya87 has posted, the joke becomes obvious: depending on keyPerPageCount, pageNumber can be as large as 2256
Let's post some theory here... It's an absurd simulation that tries to make you see how unfeasible the discussion actually is...
If you had an ASIC that (instead of creating hashes) generates private keys, and your asic generated at 100 Tk/s, your ASIC would generate 100000000000000 keys per second. Let's say you'd have 100 of those ASICs, generating 10000000000000000 keys per second... It would take those ASICs 3671743063080802746815416825491100000000000000000000000 years to generate the complete keyspace.
I've googled around, and found this bloke who was optimising random string generation on an i5 cpu. His original program created about 6000 random strings per second... People in his thread optimized his code and were able to generate a bit more, but no-one was able to generate more than 10000 strings per second... So, even the story with 100 ASIC's that were built for key creation is completely absurd. I don't think you'll ever be able to build a farm that generates 10000000000000000 keys per second, and even if you do, the earth will be long gone before they even scan 1% of the keyspace...