> Does this mean Maxima cannot do DiracDelta() calculus correctly no matter what I try?
No it doesn't mean that. If x * delta(x) / x --> delta(x) is a deal breaker, you'll need to change the general simplifier.
Of course modifying the general simplifier might introduce new bugs, break lots of code, or slow calculations. So it's
an activity that requires a great deal of care.
Arguably x/x --> 1 is an incorrect simplification; nevertheless it's possible to do useful work with Maxima, by the way.
--Barton