I'd be a time traveler who stays at home and plays LoL all day. And only leaves the house to annoy people.
Ha ha, I like it! Of course, you wouldn't expect anything less from someone with your username.
Then what is the point of having time travelling powers if you never use them?
Maybe the manga is an existential work that explores this very question. Sometimes unfulfilled potential in one individual can bring out the most in others. It is possible that never using one's powers of time travel might be the very best way to use these powers. In a sense, I feel that Shin Seiki Evangelion explored some of these very ideas.
Or maybe, the time traveller is just lazy and chose to live in a setting where being a hikikomori is a somewhat less shameful existence.
I can imagine that, lol Homu really suit that image well.
You're just Homu!
By the way, I haven't watched Puella Magi Madoka Magica yetand I never will