It is possible from a technical standpoint (look up libdvd or MakeMKV) but it might not be worth it for some titles. Here are some considerations:
➖ Pressed DVDs, as opposed to DVD±R(W)s, last very long and do not take up too much physical space on spindles, in paper sleeves or organizers (depends on your apartment size of course). Drives do fail but can be acquired cheaply (or for free if you salvage them from old PCs and have a USB adapter).
➕ DVDs will always have worse compatibility with modern equipment than MP4. Good luck getting a smart TV to play one from a drive over USB.
➕ For content that only ever existed as SD video, your non-reencoded rip will be pretty much the highest quality available.
➖ That rip will almost certainly be in SD MPEG-2, interlaced (unless it’s a movie), and gigabytes in size, usually a little over 4 or 7 GiB (most discs are single-layer or double-layer and the video bitrate is set to fill the capacity).
You can reduce file size to 10-25% by reencoding to H.264 or H.265, using a lot of computing power and losing a little quality. H.265 does not support interlacing and takes way longer to encode, but you can fit a good-looking 100-minute HD movie on a CD with it! Many pirates overestimate the bitrate they need with H.265, leading to unnecessarily giant release files.
➖ Likely not a concern for you but ripping copy-protected DVDs could be illegal even for personal use while downloading others’ HD rips might not be, like in my country.
DVD subtitles are 1bit bitmaps, ugly and relatively big in terms of storage. Their positioning is tied to video resolution so they will be at the center left if muxed with HD video. The MKV container is the only modern one that handles them at all. Converting to SRT or other text-based formats requires OCR (which does not always fully work). If they aren’t on OpenSubtitles.org, I would rip them, skim the OCR and upload them there.
➖ You will lose interactivity but that was usually more of a nuisance than a feature. I don’t think Bandersnatch or another similarly suitable title ever released on DVD. (Yes, I am confident that DVD Video is just barely capable of holding the entirety of that movie’s footage with full interactivity and everything but I doubt Netflix bothered, it would have cost a fortune.)
I would definitely back up niche DVDs but not mainstream ones – depends on how much you trust the scene to have your back. Up to you, really.