Yes. Now that all the consoles have ssds, devs are going to design their games around them. That means asset streaming is the norm. And that means hdds will cause massive pop-in and stutters.
Honestly if you don’t have an SSD save 50$ and get one. Especially for crappier pcs it’s the most significant upgrade you can do and not even for gaming. 10 years ago SSDs were somewhat niche. They were expensive as well. Now I won’t even touch a computer without one basically.
It's probably not 100% necessary; even Ratchet & Clank: Rift Apart (which was designed to use the PS5's fast loading speeds to switch between worlds on the fly, and supports the latest DirectStorage implementation on PC) can be played off a hard drive, tests have shown. But any PC recent enough to play Starfield on really should have an SSD.
"Playable" and "good experience" don't necessarily mean the same thing though. Those rift transitions in R&C are rough on anything less than a decent NVMe SSD. Though there may be some room for improvement, as even high end NVMe drives struggle to handle these transitions as gracefully as the PS5.
Whether or not playing off an HDD is truly a dealbreaker though depends on where in gameplay the storage speed bottleneck causes problems. For Rift Apart, it's mostly just an issue with these rift transitions, and the gameplay effectively pauses while it waits for them. For an open world game it could be more problematic (i.e. pervasive traversal stutter during combat.)