You do it only once, do not risk having to do it when being on a metered or spotty connection because your cache is not warm or the webmail got yet another update, which can happen at any time. You can apply Thunderbird updates when you are on a good connection.
You can access your mails offline, you don't re-download them each time you open them. It's faster, even on a good connection.
> configure
The configuration part for most providers is essentially typing one's email address and password, so there is not much to say.
> allow unlimited access to your computer
That is why I am reluctant to run non-free software, but Thunderbird is free, I can reasonably trust it. Especially the version packaged by my OS vendor. I agree a better isolation for native desktop apps may be desirable though.