I quite strongly disagree with this. Mathematicians aren't rigourous just for the hell of it. We have examples where a lack of rigour caused a bunch of people to waste a bunch of time working of stuff that ultimately didn't work at all.
Part of the purpose of a maths degree is to teach the students the rigour required to be a mathematician. If you don't want to learn that rigour then thats completely fine, you can use physical or intuitive arguments, but the place to go and do that is in the physics or engineering departments.
I agree mathematicians would be wrong if they were forcing their rigour on physics students or whatever, but I think they're emphatically right to teach it to maths students.
On the other hand, if you want full and complete rigor that means formalizing things in a computer-based proof checker. Now, that can often reveal ways to refactor the argument into a cleaner, more elegant, more intuitive proof, which is why full formalizations are often regarded as publishable work - but the other side of it is that dotting all the i's and crossing all the t's does take a whole lot of effort since some published proofs are not nearly as clear as they're supposed to be.
I agree that some published proofs are not as clear as they're supposed to be, but I disagree that formalizing things in computer-based proof checkers is the way forward there. Computer proof checking is cool, but its an augment to what we already do and not not a substitute for it.
The purpose of a published paper is to explain things to other humans, while that of a computer formalization is to explain things to computers. Just as it is generally not easy for a computer to understand a published proof, it is usually not easy for other mathematicians to understand the code you feed to Lean or whatever.
The stuff you need to focus on to get a computer to accept your proof is usually quite different to the stuff you want to focus on when explaining things to colleagues. Roughly speaking we care about why you're doing things, while the computer cares about the intricacies of what you're doing.
For example the Italian school of algebraic geometry caused the waste of legitimately decades of work by many people because the foundations weren't right: https://en.wikipedia.org/wiki/Italian_school_of_algebraic_ge....
Part of the purpose of a maths degree is to teach the students the rigour required to be a mathematician. If you don't want to learn that rigour then thats completely fine, you can use physical or intuitive arguments, but the place to go and do that is in the physics or engineering departments.
I agree mathematicians would be wrong if they were forcing their rigour on physics students or whatever, but I think they're emphatically right to teach it to maths students.