I'm looking at replacing my commuter bike with something with a big less aggro geometry (currently a GTR series 3).
I've looked
Salsa Casseroll
Redline Metro Classic https://www.redlinebicycles.com/bikes...-metro-classic
SOMA ES
surly pacer
Surly Cross Check
They all seem to have probably a bit less of a racer style geo but still very bent over it seems with fairly short head tubes.

I'm wondering, is it possible to make the handlebars higher with spacers or something on these bikes? Is there any downside to doing this?

They probably come with a decent amount of steerer tube on them with spacers under the stem. You could run a 17 degree stem turned upwards to raise the bars more if needed. And I think there are steerer tube extenders for aluminum steerers you could add on. Just guessing here as I don't own any of those bikes personally...

You might not be able to tell from the pics, but some bikes have longer head tubes than others, and even just an inch can make a big difference. I have friends on race geometry bikes who run their bars pretty high with just the stock equipment. If you can test ride at a local dealer, that could help narrow it down for you...

If nothing else, you can buy a stem riser & use that. I added one onto my Trek & it's great. It gives you an extra 1.5 or 3" (I forget which it was now, but it was plenty for my needs). Mine was a Delta brand & cost $30 from Performance bike.