It’s your bench, so the ultimate decision is up to you.
I’ve worked off a 2×4 stud bench in my uninsulated garage in Texas for years now. Temps swing from 12-120F (-11-49C) in there over the year and I haven’t had any problems. You’ll probably re-flatten the top after about a year, but that’s it.
Unless you have the setup (machines) necessary to process the large number of cuts you’ll have with the sheet goods, I’d call it unnecessary. Birch ply is also exceedingly expensive where I am. I’d choose spend my money on other items.