That said, the very idea of a "favourite" key-signature is broadly analogous to that of having a "favourite" composer, which says it all, really
I'm not entirely sure it says it all - nor would I agree with your analogy ;)
That's OK; I would no more expect broad agreement on the principles of such a topic as I would expect the majority of listeners to have a favourite key-signature!
The concept of key-colour is very well established, and not nearly as random as you suggest.
Ah, yes - synasthæsia; the two fundamental problems here, however, are that (a) not all listeners and musicians posses - or are conscious of possessing - this faculty and (b) those who do possess it do not all make the same colour/sound relationships.
How any keys are there? 24, major and minor. But how many composers are there, from whom to choose a favourite? ;)
What you write about here is by definition confined to Western major/minor modes of relatively recent origin, to tonality, to reliance upon the establishment of a pitch system in which A = whatever it does and to a system broadly reliant upon equal temperament in which an octave is divided into 12 equal semitones so, for those four reasons, one could argue that it is universal neither globally nor historically.
Not only that, key-signatures as such relate to particular ways and means of "spelling" with what we might call "conventional" musical notation yet, even within these confines, questions inevitably arise because, as we use only 7 different note names within a 12-semitone notational system, enharmonics apply; what, for example, might you say about two people of whom one claims a favourite key-signature containing six flats when another claims one containing six sharps?
Then there's the question of whether and when to use key-signatures at all, even when writing music that is broadly tonal; for Schönberg not to have used the key-signature of E flat major (and equivalents for the orchestral transposing instruments) in the opening pages of
Gurrelieder would have been as absurd as it would have been clumsy, yet what price the D minor one in the first few minutes of his String Quartet in that key? With that in mind, I am bound to question what having a "favourite key-signature" might even mean at all, other than that it would presumably mean different things to different people...
If you're going to the George tomorrow, you could tell me more about it then?
I won't, I'm afraid but, as the above hopefully demonstrates, that doesn't in itself mean that I prefer not to say anything on the subject!