There are a couple things I consider when choosing time signatures. I don't write music quite like this but I can see a few reasons why something like this might take place.
Generally speaking, it is easier to maintain a tempo than to switch. So when a composer is going from one time signature to another, it is easiest to maintain the tempo and use different subdivisions to spell out your new time signature, rather than changing the tempo to keep the time signature easier to read within. This tends to make more sense when the piece frequently changes time signatures and less sense when the piece changes from one time signature to another that will last for an extended time.
This next part is not exactly a standard convention within the tradition but seems to be generally followed in many settings and makes intuitive sense to most I speak with about it. I like to make the distinction between different denominators within a meter. A simple example: 4/4 and 8/8; 4/4 is best used to describe a standard rhythm with 4 beats, while 8/8 is the same amount of eight or quarter notes, it is best used to describe groupings within that time that amount to uneven beats.
4/4: 1 + 2 + 3 + 4 +
8/8: 1 + a 2 + a 3 +
Let's translate this concept to another meter: 5/4 vs 5/8. I think of 5/4 as having 5 equal beats (1/4 notes), while 5/8 would have 2 uneven beats with 3 and 2 eighth notes.
5/4: 1 + 2 + 3 + 4 + 5 +
5/8: 1 + a 2 +
So when starting from scratch and trying to choose a meter, I would base my choice on the beats. Once a piece is established, your choices become a little different but the same concept can apply. It may be best to write something in one meter to maintain tempo, or it may be best to change your tempo to accommodate the new feel of your change in meter. For instance, going from 4/4 to a sort of double time, it may be best to write 4/8. This allows the measure to maintain 4 beats without needing to specify the double time and by not maintaining the length of a bar (4 1/4 notes) we do not introduce the confusion of an 8/8 time signature, which would imply the uneven beats as described above. This would also apply to double time in 3/4, where switching to 6/8 (maintaining the length of the measure) would imply a change in the length of the beat (6/8 is nearly always 2 beats of 3 eighth notes, which would subvert the intention of double time). Again, this will largely depend on how long this new meter will be utilized. It will ultimately be easier to read something in 4/4 than 4/8, especially if there are a lot of subdivisions, so changing the tempo to write 4/4 would be preferred if the double time would appear for an extended time.
As others have suggested, it sometimes seems that composers have taken this approach to be more complicated or just because they can. However, when listening to some composers, it just makes sense. Think of Stravinsky. In The Rite of Spring the meters change all the time but when I listen to the piece it just sounds right. I also tend to think that a lot of people don't fully understand a piece of music when they make some sort of judgement about whether or not the use of certain time signatures is justified. There is always some sort of intent. I have conceptualized writing a piece that would include what would normally be considered poor choices for meters with the intention of making it harder for the players to read, which could add the effect of chaos or confusion, allowing it to convey an intended feeling when performed without directing the players as such. I have seen a performance of a piece that has a similar approach with a little more depth of concept, Failing. The idea being that the piece is intended to be difficult for the sake of being difficult, with the additional depth being that the intention of the composer is to have the performer fail and by successfully performing the piece, you are also failing.
In the piece that you are analyzing, it seems that nearly all of the measures with less than conventional meters start with a rest (not all though). So it appears that the Sciarrino wanted a specific space to appear between phrases that would not be properly accommodated by a rest at the end of the previous measure. This also allows the piece to maintain a feeling of being off of the beat, though nothing at the beginning seems to provide a pulse to be off of, the off beat feel will be translated by the performers. I would argue that the use of the time signatures in this case would be somewhat to space out the phrases. Similar circumstances could be an instance where another composer may employ a fermata but by adjusting the time signature and adding a rest would specify the length, though in this case nothing is being sustained.
There are lots of reasons one might choose to have complex and changing time signatures but it is generally safe to say that it is not arbitrary. Specifically to the point of x/4 vs x/8, there can be larger implications than readability, including beat allocation within a measure/subdivisions of beats as well as preserving tempo, which can ultimately be more readable. As a final note, I wrote a lot of music that was essentially free of meter, as in it would constantly change meter if analyzed by phrases. My composition teacher, the late Dr. Packales, advised me once that leaving the pieces in 4/4 as I did may ultimately be easier and more readable for the performers. I liked the idea at the time because it made me feel unique or something but in the end, a lack of time signature changes would more likely leave the performer needing to analyze the piece to determine not only phrasing but beats, making it harder to get a proper feeling for whether something takes place on a downbeat or an upbeat etc.
