The 3-chloroperoxy benzoic acid is a stable crystal
People I know generally refer to it as "meta-chloroperbenzoic acid" or MCPBA as Chromic calls it. Stability is a relative term, the stuff I have worked with had a tendency to fume off if it wasn't stored in a freezer.
that doesn't have to be prepared on the spot.
If you can buy MCPBA you can also buy premade peracetic acid or you can buy 100% formic acid or acetic anhydride and 50% H2O2 and easily prepare your own performic and peracetic acids.
It's generally a lot safer to handle
I'm not so sure about that.
There isn't any nasty waste to deal with, the side product is simply 3-chlorobenzoic acid.
Formic acid, acetic acid and their peracids would be seem to be much more biodegradable than meta-chlorobenzoic acid, just dump them down the toilet.
MCPBA is used when epoxide only is desired. For our purposes a mixture of glycol and epoxide is fine so there does not seem to be any advantage to using MCPBA.