General :: Blocking Or Sleeping An Interrupt Handler?

Assume: 1) Multi-cpu environment 2) Process that gets interrupted, is the same process that executes the interrupt handler, so I guess technically nothing gets interrupted except what the process was doing before, but it is still executing as it is executing the handler. 3) There is no top or bottom half, when an interrupt takes place the handler is invoked, executes, then return from interrupt, simple as that.

Why would sleeping the handler (puts in sleep queue, context switch to next runnable process) be a bad idea?