I'll give the dissenting opinion here.

I cut the Phalaenopsis flower stalks off when the flowers die (or most of
them have died). I cut it back to the plant (leaving about 1/4 inch stub).
I do this because I don't want the plant wasting energy pushing out a few
flowers that usually don't display well. I'd prefer the plant use the
energy to put out a couple of leaves and build up strength. I want bigger
or more flowers next year rather than an extra flower or two.

One year I did not cut the old spikes. In September the plants started to
put out a few flowers on the old spikes and did not send up a new fresh
spike for the new season. Now I cut them all.

Of course this doesn't apply to many of the species that rebloom for years
on older spikes. I also don't cut spikes that have begun to keiki.

Good Growing,
Gene