is having a scratch disk necessary?

If your system drive is an NVMe drive, you should definitely have your scratch disk there (as long as there is enough space). These drives are so insanely fast that RAM almost becomes irrelevant.

The general advice these days is that with SSDs, there's no speed advantage to a separate scratch disk, since there's no moving read/write head.

As others have said, it is not a question of would you benefit from scratch disk rather Photoshop will not function without it.

I have 64GB RAM here and still end up with large, sometimes massive, scratch disk files depending on what I am doing.
As to whether you can use the OS disk, you can, and many with only one disk do this. But given a choice, a separate disk is better. That way the scratch disk file will not be limited by the space on your OS disk, nor will it impinge on the space available for your operating system on that disk.

It's a sort of sef defeating question.  If you feel the need to ask it, then it suggests your hardware specs might possibly be marginal, but if yourware is marginal, you have a greater need for scratch space.  If you only have the one drive, then that's the one Photoshop will use.  You can't untic all available drives.  Photoshop won't let you.

If you were using Windows I'd suggest some ways to save space on your boot drive.  There must be similar information for OSX systems.  I found some links with Google, but it's something I'd want reliable advise on before trying.

Photoshop moves so much data around that it can't be held in RAM. No matter how much RAM you have, it's not enough.

So temporary working data are written to your hard drive. That's the scratch disk. Either the system drive, or another physical drive of your choosing. For Photoshop, RAM is more a fast access cache for the scratch disk's main memory.

Photoshop can't function without enough free space for the scratch disk.

Try: https://helpx.adobe.com/au/photoshop/kb/optimize-photoshop-cc-performance.html