No. The easiest way to understand why that is so is to explore the alternatives. It's a lot easier to keep one password (which might include two factor auth) provably secure than several. I don't have to plan for my LastPass password getting broken since it's heat-death-of-the-universe-unfeasable for someone to break it. Thus the risk management is at an optimum.

You don't gain security if you split it up - only obscurity. Increasing the number of different passwords someone needs to remember also increases the risk for people to invent "password schemes", which all lessen security due to lowering entropy.

A lot of people who should know better fail at understanding entropy. I recently had a debate with someone whose current job position is "security architect" (my own background is in crypto and security, but I don't work with it today) who didn't like our choice of 128 bit UUIDs as authentication tokens in URLs. He believed we should add a unique string for our specific service in front of the UUID, to lessen the risk for clashes with other services.

Bitcoinica using LastPass wasn't a problem. Using a known string as master password was.