Why is it deemed necessary to put the key signature at the beginning of each line? And in the same vein, why do we need a time signature at all, when it's fairly apparent what it will be in the first bar or two? Or, a slightly different slant, as common time is so common, use that as default, and only write in other time signatures.
The time signature cannot be figured out from the content since both 2/2 and 4/4 have a whole note all-in-all but have different accents and drive. It's even worse with 6/8 and 3/4.
The repetition of the key signature is just a visual reminder since the key signature pervades a piece. If you start the piece from the second page, it would be really awkward to have to leaf backwards in order to figure out what notes to play. Having each line "grounded" in its key signature makes it easier to be sure about what one is playing.
Arguably that would also hold with the meter. Convention still has converged to not repeating it, just like one does not repeat a tempo mark like "Allegro".
Sure, you can generally discover the time after a few bars. But why not know it BEFORE the first note? It will make more sense of the conductor's upbeat when sight-playing, if nothing else.
There's a "fake book" style where after the first line not only time signature but also key signature and clef are omitted. It's not helpful, particularly in e.g. a Broadway pit orchestra part where both key changes and cuts are common, so you can find yourself cutting into a different - unstated - key! Some old-timers find the style "professional", though I think the only professional aspect was corner-cutting by paid-per-bar Union copyists.
Even in cases where you can figure out the time signature (there are cases where you can't), the part is not supposed to be a puzzle. It's supposed to make things as clear as possible to the player.
Key signatures can often change so it's good to be reminded at every line what the current key signature is. Sometimes, on lead sheets of simple tunes that have no key signature changes, it's only written on the first line.