Well, the thing about dogs, is they require a lot more room than cats.
I have 2 black labs and they run and run and run and run. If I didn't have so much room outside, I couldn't handle them.
OTOH, you can pretty much get by having 1 room per cat. So although I only have like 3 rooms, it's big enough for my 3 cats (I don't let them outside).
I'm not sure cats like being left alone. I mean, you can, unlike dogs, but in my experience, cats get awfully lonely, too. When I was in college and just had the 1 cat, she would always greet me at the door, and would always be by my side when I was home.
And I feed several stray cats. They often want to get petted more than to be fed.
Cats just tend to have more pride (and dignity) than dogs, and don't like to admit they are lonely.