I don't see any fundamental difference using python or curl (shrugging emoji).
In both case, the goal is to access a page while being connected. Of course, the syntax is different, but basically, the idea is the same. How you use the html after that is another story, but the access part is quite similar. If you would like to test it again in python, you can pm me what you did, and I will try to help you!
In my case, when I run one of these programs, I run it on a different session than the browser one and that's all.
I'm currently using python for this, before I used a curl equivalent. The only reason why I changed is my current "favorite" language(s).
I think Philosopher asked this out of curiosity, not because the pain of relogging was unbearable - at least, that is how I understood the question.
In my opinion, the logging problem is not big enough to justify using the Chrome's console. Of course, I'm not saying you shouldn't use it; I'm just saying this thing only is a too small criteria by itself.
Obviously, that's no more than my personal opinion, and I agree with the fact you feel otherwise :)