You can write proofs along with the course, and since they are machine checked you can have confidence that they are correct.
If you don't know, writing a proof in isolation can be difficult, since you may be writing on that isn't actually sound.
If you don't know, writing a proof in isolation can be difficult, since you may be writing on that isn't actually sound.
I just think this is a distraction unless your goal is to learn lean and not math.
Errors are found in human proofs all the time. And like everything else, going through the process of formalizing to a machine only increases the clarity and accuracy of what you’re doing.
Over-emphasis on formalism leads me to conclude you just don't understand the purpose of proofs. You are primarily interested in formal logic - not math.
I would invite you to read a few pages of famous papers - for example Perelman's paper on the Poincaré Conjecture.