That is a good idea. It's really frustrating when a video disappears. Even more common on Twitter and other social media when a post gets reported or an account suspended.
The guy who made the overhead drone videos asked for acknowledgment when one of his videos was downloaded and clipped without attribution. The clip was to highlight footage of the "Attack of the 50 Foot Drag Queen".
So he might be OK with his videos being re-uploaded with acknowledgement?
https://mobile.twitter.com/SimonRAnderson1/status/1639864192437194752
Sometimes it is hard to know who shot the original video, as in the case above. That clip was taken from a copy that someone else had made without attribution.
This is all off the top of my head from memory so best to check the content in the linked articles in case I have got anything wrong:
If someone does "claim copyright" when a video is re-uploaded to YouTube then you might get a "copyright strike" (three strikes and YouTube nukes your Channel).
Copyright claims and copyright strikes are different things:
https://tuberanker.com/blog/copyright-claim-youtube
However, you get the opportunity to contact the copyright owner who has complained, in order to request permission to leave the copy up.
https://support.google.com/youtube/answer/7002106?hl=en
It's mostly big companies like Warner Bros that are arses and refuse permission and get YT to delete videos they claim. In one notorious case a woman who demonstrates crochet techniques had her video deleted because there was a radio playing quietly in the background. One of the songs played for about 15 seconds was copyright to Warner Bros so they claimed copyright of her video and had YT delete it.
If it is a normal, sensible person they will probably let you keep the video up as long as you agree to their copyright claim, which enables them to receive any advertising revenue accrued from views of the copy on your Channel.
As part of the process of uploading there is an automated check to see if the material is copyrighted:
https://www.trustedreviews.com/how-to/tell-if-youtube-content-is-copyrighted-4129385
IIRC there is a privacy issue with the copyright claim process. Remember that creep Yaniv? IIRC the channel's email is shared with the copyright claimant - I can't find confirmation of that but there is something in the back of my mind about JY obtaining contact details of channel owners via the copyright claim system.
There are easy ways to download YT videos here:
http://deturl.com/
For Twitter and other social media platforms, do an internet search for, eg. "Download Twitter video" and there should be several options in the search results.