Here's an easier to understand query for what you're trying to do (at least it's easier to understand for me):

    cat input.json | jq -r '(first | keys) as $cols | $cols, (.[] | [.[$cols[]]]) | @tsv'

That whole map and from entries throws it off. It's not a good use for what you're doing. tsv expects a bunch of arrays, whereas you're getting a bunch of objects (with the header also being one) and then converting them to arrays. That is an unnecessary step and makes it a little harder to understand.