I'm a bit surprised by the answers you've received. Time signature is not a purely mathematical phenomenon. It is often a matter of convention mixed in with convenience. Most of all, it's about the communication of information.

IMO, 12/8 will generally lead someone to expect triplets grouped into square time, because that's how certain Baroque dances/compositions were published. 12/8 yields an easy, straightforward, uncluttered way of preparing the manuscript for that kind of meter. It also saves ink. You'll also see some Baroque pieces notated in 9/8, which just indicates triplets grouped into triple meter, and not some fancy 4-3-2 grouping.

I strongly doubt all of this was standardized until these manuscripts were printed in the 20th century, after recorded music revived interest in the Baroque era. When these pieces were composed, the communicative intent of the manuscript was different, and everyone knew what characterized a gavotte, sarabande, etc.

You could group 12 eighth notes any way you like. But then you would need to notate those groupings explicitly, whenever you're not following a well-established convention.

I would also argue that there is no particular convention around 6/4, as opposed to 6/8, which usually indicates triplets grouped in a sort of 2/4 meter. Really, multiples of three in time signatures primarily exist in manuscript to eliminate explicit triplet markings. To me, 6/4 would make sense in a piece with mixed meter, or in a very slow piece in which the duration of the quarter note has been previously established, as a way of indicating that something doesn't feel like it's in triple meter, or something along those lines.