Question: Would a Great Pyrenees or Maremma make a good indoor house pet if I gave it exercise?
Most likely, no. Those breeds don't want to be a house pet or part of your family. They've been bred for years to live outdoors and guard livestock (like sheep and goats). Keeping them as house pets usually causes them to have behavior problems and be destructive.
I'm usually against keeping dogs outdoors, but these breeds have been genetically hard wired to do this. The happiest G.P. dogs I know are ones that get to stay outside and watch their "flock".
They generally don't get along with more than one or two people, don't have much patience for children or smaller animals, and will demolish a house when they get upset.
It's not really a matter of exercise. It's a matter of a dog breed doing what it was bred for. If you want a large house dog, look into a Great Dane, Rott, or Mastiff.
I'm sorry if this sounds harsh, but seven years as a vet tech has taught me that some breeds of dogs are not suited for some situations and it just makes things harder for the dog and the owner.