Not true. I recommend Five Stages of Accepting Constructive Mathematics:
Par for the course for computer scientists - if we had infinite time/space we wouldn't have to optimise anything.
This paper  by Ed Nelson presents a brilliant analysis on the difference between classical logicians and intuitionists.
It starts with a crucial distinction in semantics.
Assuming ∀x¬A and arriving at a contradiction not a proof for ∃xA.
And yet, simply on the grounds of utility, the intuitionist perspective is far more useful to me as an every-day philosophy simply because "incomplete communications" is a mental model of how human systems/interactions work and how information flows in general. That which we call knowledge is socially constructed  and is always incomplete.
But you are are aware of this already, I'm just writing it out.
Look at these provers, they're almost all based on classical logic, and even on proofs by contradiction:
Even Isabelle/HOL, which is quite user friendly and has a lot of automation (like Sledgehammer, which can call to the automatic provers mentioned above) is based on classical logic with choice.
But you also end up with proofs that are much, much shorter.
I guess it's all about the degree of uncertainty. Constructive mathematics reduces the degree of uncertainty, which grows exponentially as you get in the higher level proofs.