I've worked for 5 very large companies and one startup. I'd say if you have a critical role in the company and aren't "just a dev/tester etc" you wouldn't have

I've worked for 5 very large companies and one startup. I'd say if you have a critical role in the company and aren't "just a dev/tester etc" you wouldn't have a problem getting private space when you need it. I've often found programme managers or senior architects can get a room for large periods of time or project teams of 3/4 people can get a space for a number of days/weeks/months for critical projects. I'd be surprised if this works differently anywhere else but the default always seems to be cubes