Let's do a thought experiment.
Let's assume we just never got hard drives to work all that well, head crashes are common and large storage capacities are only possible in servers with incredibly expensive anti vibration setups and what not and there's no way they'd ever work in portable devices. And optical media just didn't work out. Maybe somehow we didn't discover the science in time and the companies working on it just failed or bad management decisions killed off the research into it before anything useful came off of it. And flash storage just never came down in price.
How far could we have pushed cassettes and tape if all the effort that went into other technologies had to be put into cassettes because there simply wasn't a good alternative for data storage. What are the limits of how fast we could move tape in a cassette? How miniaturized would the technology be by now in 2023? I know that there are contemporary tape backup systems with large capacities but there hasn't been any efforts into high speed seek times or making cassettes a viable tiny medium for use as removable media on PDAs or mobile phones.
If we could pack data densely enough and move the tape quickly enough how possible would modern computer tasks like high resolution digital video or image editing be? Assuming that we still had the high speed processors and non-persistent memory of the present but just no other data storage medium aside from magnetic tape.
For inspiration consider that in 1992 we had NT Cassettes that are about as big as an SD card an could store nearly a Gigabyte and in the enterprise LTO-9 tape (released in 2021) stores around 18 TB. So it doesn't sound impossible to have tiny cassettes with a lot of storage if we spend the last 3 decades working on it.
There are hard physical limits on tape; you can only make it so thin (ie; pack so much tape in a space) before it becomes too prone to snapping. You can only run it so fast before it becomes too prone to snapping. You can only change direction so fast before it snaps from the strain.
Fancy data storage and compression algorithms only get you so far. Barring ridiculous materials science advances for the substrate, I feel like the only real way to make it work would be to have massive amounts of RAM (probably battery-backed SRAM). Load the entire tape into a dedicated ramdisk and use it more or less the same way we use USB media now; data transfer that you have to safely eject (write back all changes).