Downloading files overnight on your computer is safe to do and I do it all the time especially when I have large files I need to download or upload.
If I have large files that I need to download or upload I will let them upload or download overnight when I'm asleep and when I wake up the files are uploaded or downloaded.
There's nothing bad about leaving your computer on all night especially if it's a desktop computer and my desktop computer never gets shut off at all unless there's a power outage or I shut it off and unplug it to work on it or clean it.
My desktop computer otherwise stays on 24 hours per day 7 days per week just like a web server stays on all the time without being shut off.