The problem with using the same password on multiple sites is this: if any one site gets pwnd, it gets a lot easier for the cybercreeps to pwn your account on other sites (says Obvious Man).
It doesn't take much technical skill to credential-stuff--to hammer a lot of sites with a list of credentials. So, keeping the list of sites you actually use a secret is not effective.
This whole deal sucks. But it's real.
As for the password strategy, I imagine you could be vulnerable if any two important accounts - say, email and bank - both used the same password. Are you confident this is not the case?
I assume certain emails associate with certain types of accounts, which could flaw your strategy. If you're able to remember ~15 different passwords with random emails, congrats on your stellar memory!
I currently have about ~15 different passwords I use. I know which to use based on how long I've been using the service. Why is this strategy ineffective?? At most a hacker could get 3-4 of the services I use, and even then they'd need to find each of those services out of the hundreds I use. I also have 4 different emails I use for logins.