Hi Lawrence:
One way some teachers have it both ways is to put put all extra credit into one category, say essays for example, which may be worth 25% of their grade. Once that 25% category is filled up, no more extra credit (becasue there's no place to add it). So although the student may may performed poorly in the past, they are given a smidge of opportunity to make up for it - but not a lot.
Some institutions have existing policies that either mandate or forbid use of EC. Teachers at these institutions just have go along with the program.
Regards, Barry