Is it possible to have a cryptocurrency based on email address?
With Bitcoin and its derivatives, you can already generate a private key any way you like and import it using the importprivkey RPC command.  You may start with any 256 bits of data (i.e. any number between 0 and 2^256-1), convert it to WIF format as explained at https://en.bitcoin.it/wiki/Wallet_import_format, and import it.

However, don't start getting attached to this idea before you understand things better.  


  I just don't like the fact that cryptocurrency keys are randomly generated. Even though I know generating such a pair again is almost impossible. I don't like it because it's "almost" impossible.


The solution to this is not to invent something new - the solution is for you to learn more math until you are convinced that it is reasonable.  This is the case with everything in cryptography: no attack can ever be made impossible.  But making it sufficiently improbable really is close enough.

If you generate a private key some other way besides randomly, it makes it a lot easier for someone to guess it and steal all your money.  There used to be a fad called "brain wallets" where you would make up some memorable phrase and use it as a private key.  People who did this got their money stolen routinely, because the number of memorable phrases you might come up with is relatively small, and it's very easy for someone with a good computer to just try and guess all of them.  But the universe cannot support a computer good enough to try all 2^256 possible random keys.