Rigor is the whole point of math. The moment you start asking if there is too much of it you are solving a different problem.
Rigor is one solution to mutual understanding Bourbaki came up with that in turn led to making math inaccessible to most humans as it now takes regular mathematicians over 40 years to get to the bleeding edge, often surpassing their brain's capacity to come up with revolutionary insights. It's like math was forced to run on assembly language despite there were more high-level languages available and more apt for the job.
If rigor is the whole point why are we so focused on classical math (eg classical logic) not the wider plurality?
It seems you have never tried to prove anything using a proof assistant program. It will demand proofs for things like x<y && y<z => x<z and while it should have that built in for natural numbers, woe fall upon thee who defines a new data type.
Rigor is not the whole point of math. Understanding is. Rigor is a tool for producing understanding. For a further articulation of this point, see
https://arxiv.org/abs/math/9404236