My wife and I personally think it's borderline inhumane to keep a dog by itself all day, since they are extremely social.
While we usually don't keep solitary cats, I don't think it's that uncomfortable for cats to be alone, though per your DM interpretation, they will commonly get into things. Which they will do in groups too.
The amount of desired human attention sought from cats in our household has has decreased as the number of cats in the has increased. That's not to say they don't still want our attention, or that we don't give it to them. Having friends to keep busy seems to make the days go by easier.
When the boy went to be neutered, the girl spent the whole day going from room to room meowing and looking in his usual spots.
When she went to be fixed, he did the same.
I'll probably never have a single cat again (some of that is that they are used to each others presence I'm sure) since they are excellent company for each other.