But it is easy to present deep ideas from constructivism, without mentioning the word constructivism. Or even acknowledging that the philosophy exists.

For example the second half of https://math.stackexchange.com/questions/5074503/can-pa-prov... is an important constructivist thing. It shows why everything that a constructivist could ever be interested in mathematically, can be embedded in the natural numbers. With all of the constructions needing nothing more than the Peano Axioms. (Proving the results may need stronger axioms though...)

From my point of view, https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach does something similar. That book got a lot of people interested in basic concepts around recursion, computation, and what it means to think. Absolutely everything in it works constructively. And yet that philosophy is not mentioned. Not even once.

The only point where a constructivist need discuss all of the philosophical back and forth on constructivism, is in explaining why a constructivist need not accept various claims coming out of classical mathematics. And even that discussion would not be so painful if people who have learned classical mathematics were more aware of the philosophical assumptions that they are making.