Alan Beban wrote...
....
There is no question that each search can be accomplished with the use
of relatively simple but individually tailored built-in functions. But
that seems beside the point of the original posting, which suggested
that a simple function, of the nature of

COUNTU(Rng, Criterion)
....

The problem is there's no end to what could be valid criterion
arguments. The ideal would be accepting COUNTIF/SUMIF-like criteria,
but that'd lead to multiple criteria issues.

There comes a point when it makes no sense to customize a function any
further. Generally, as general as possible is best. A rich set of
criterion strings is arguably going too far. Also, there are times the
best response to OPs is 'what you want to do could be done better . .
..' IMO, this is a situation in which the flexibility of subexpressions
is clearly preferable to the rigidity of elaborately specific udfs.