If you do notice that the same issue is occurring, there is a checkbox (lower left) of the dialog when reporting that says that the same problem will be ignored. That’s probably better than removing apport itself.
Without apport reports on launchpad - no developer or tester will be aware of any issue you are having.
if “System program problem detected” warnings appear every day (and it’s annoying, I know) and if you’re sure that there isn’t any recent system problem, just take a look into /var/crash and delete old files, if any.
As fossfreedom says, it’s anyway better than removing apport.