Everyone thinks proofs are this holy grail and totally rigorous, and they are on a certain level. But the idea is floating around that Mathematicians are infallible when in fact lots of proofs in highly complex areas of mathematics are NOT 100% perfectly rigorous. They contain a lot of skipping, because "it's trivial" and consensus.
This approach may work very often, but there is a danger that sometimes it doesn't work and things get overlooked. Since mathematics is done in a bottom-up approach, at some point some fundament may or may not turn out to be wrong, which endangers parts built on top of it.
The whole movement of rigorous automated proof systems is to prove mathematics from the very bottom to the very top in a 100% rigorous and verifiable way.
Doing actual rigorous proofs a computer can verify is enormously tedious and many Mathematicians dislike it for that reason, because the inherently subjective "elegance" and "beauty" gets lost in translation.