Everyone will take advantage of it, sure, why wouldn't you? It's the same as on PCs. You have a nice and fast SSD in X1SX and then you have a crazy fast SSD with some other stuff that allows you to shuffle data into RAM even faster on PS5. So that's awesome for the PS5 and I don't in any way want to downplay how awesome that is. My example before of 5s loads vs. 3s loads might've also downplayed that - but now scale that by 10. 50s loads vs. 30s loads would immediately make a game much more enjoyable on PS5. That said, with these super fast SSDs, I sure as shit hope that nobody will build stuff that takes THIS long to load anymore, but time will tell.
Now, let's say that the average load time with those SSDs on next-gen will be 10 seconds. And let's be generous and say that the PS5 SSD and throughput is twice as fast as X1SX - At that point you'd have 10s load times vs. 5s load times (keep in mind that loading often is more than just shuffling data around, so this isn't in any way accurate). I don't know if I'd care that much about 5 seconds saved every time I load if what I give up for that is framerate or resolution. And I guess that's the bet that Microsoft made here - more raw power rather than faster data transfer.
Now, it's clear that the Sony First Party devs will design their games around the crazy SSD and ensure that everything's smooth and juicy all the time and that you don't even see loading screens at all and that's great. But assuming that third parties will change their games completely, adjust levels and other stuff just to squeeze the most out of the PS5 architecture is just nutty. It won't happen. So again, what I think will be the usual case is that you'll see X1SX games render at 4k more regularly and / or at better framerates and on PS5 games will load faster. Players will have to decide what's more important to them.
Btw, one thing that'll suck for all of us is that 1TB is just too small nowadays, so prepare for housekeeping a lot more, at least until new console iterations appear with larger SSDs. The recent Call of Duty weighed in at like 170gb... So I doubt you'll be able to have more than 10-15 games or so simultaneously on your machine. Meh.