Archive Team often uses the Internet Archive to share the things they save and obviously they have a shared goal of saving a copy of everything ever made, but they aren’t the same people. The Archive Team is a vigilante white hat hacker group (well, maybe a little bit grey), and running a Warrior basically means you’re volunteering to be part of their botnet. When a website is going to be shut down, they’ll whip together a script and push it out to the botnet to try to grab as much of the dying site as they can, and when there’s more downtime they have some other projects, like trying to brute force all those awful link shorteners so that when they inevitably die, people can still figure out where it should’ve pointed to.
“Lossless” has a specific meaning, that you haven’t lost any data, perceptible or not. The original can be recreated down to the exact 1s and 0s. “Lossy” compression generally means “data is lost but it’s worth it and still does the job” which is what it sounds like you’re looking for.
With images, sometimes if technology has advanced, you can find ways to apply even more compression without any more data loss, but that’s less common in video. People can choose to keep raw photos with all the information that the sensor got when the photo was taken, but a “raw” uncompressed video would be preposterously huge, so video codecs have to throw out a lot more data than photo formats do. It’s fine because videos keep moving, you don’t stare at a single frame for more than a fraction of a second anyway. But that doesn’t leave much room for improvement without throwing out even more, and going from one lossy algorithm to another has the downside of the new algorithm not knowing what’s “good” visual data from the original and what’s just compression noise from the first lossy algorithm, so it will attempt to preserve junk while also adding its own. You can always give it a try and see what happens, of course, but there are limits before it starts looking glitchy and bad.