Q:

Why are time signatures not used in this score?

I was looking at this hand-written short score (to be completed by other arrangers):

The only thing that strikes me about it (maybe there should be others) is there is no written time signature. Why?
Then I had the following thoughts. Please correct me if I'm wrong.
The beaming notation already implies where the beats are. And the bar-lines separate and indicate how many beats per measure. So in essence, you could infer exactly what the time signature was? It also seems like the time signature changed several times, based on this premise.
In other words, most (perhaps all) time signatures are redundant; because they are directly implied through the other notation (especially if ties and beams are used rigorously).
This would also mean a performer wouldn't even need to see a time-signature, as long as he/she is reading ahead and taking note where the beams and ties are- he/she will know when the beats occur.

A:

This free-thinking question has already provoked at least
one thoughtful answer.
The sample score happens to have time signatures, however,
beginning with 4 bars of 4⁄4
and going into a bar of 2⁄4
before returning to 4⁄4 .
They're just stretched beyond recognition.

Squashed (unstretched):

Close-in to unstretched 2⁄4
and 4⁄4 :

Not that it changes the question . . .

A:

Here's a pathological example:

Is this in 3/4, or 6/8? They have different emphases, so it's not an arbitrary distinction. And the tune might even use both. I'm looking at you, West Side Story.
I could also bring up 4/4 and 2/2, or Common and Cut Time.
Now, you may say that in most normal pieces, the beaming and/or tempo would give that away. I might observe that beaming is not a particularly standardised art, but it's a reasonable point. So, why do we notate the time signature?
Let's ask the same question about key signatures. Here's a nice little tune:

Bit of a pain to read, though. My brain has to individually process each note, and deal with all those flats. I like this version better:

It's easier to read. My brain does less work, because I can immediately assume that all of the non-stupid flats1 are in use.
Time signatures perform a similar function. I don't want to have to precount all the bars to figure out what time signature I'm dealing with. That's inefficient. And rather difficult if the time signature changes even occasionally.
So, to answer your question, yes, you can possibly omit the time signature, and still have 'readable' music. However, you shouldn't, for the same reason that you shouldn't write everything in C Major with loads of accidentals.
[Note 1] Apologies to any friends and/or relatives of C♭ and F♭. You have my sincerest condolences.

