Independant tanks give you the ability to access gas in the afflicted tank in the event of a regulator failure - you close the isolator to isolate the unaffected tank from the compromised tank, switch regs (if necessary), close down the post with the failed regulator, and reopen the isolator.
With independant tanks, if a regulator fails, the gas in that tank is either inaccessable if you close it down, or lost rapidly.
There are also trim issues with independant tanks - my understanding is (never having dived them) that if you breathed one tank down fully before switching, then you're going to be several kilograms lighter on that side, and be inclined to roll the other way. Independant doubles divers claim that if you can't switch regs periodically to counteract this, then you shouldn't be diving doubles, but with a manifold, switching regs is eliminated entirely.
Independant doubles still might pop up in your configuration though if you want to dive doubles at some vacation destinations, and you twin two rental tanks.