It really always stroke me as the "default" gaming when you try to have pretty much everything in your team. I guess both the anime (Ash has always had type variety in his teams) and role-playing/character-building customs themselves affect to this thinking of mine (and many others'). So, I think even intuitively, you try to have as many types of Pokémon in your team as possible. Or at least a couple of different types. You kind of have to be over an invisible limit of what you feel is a "safe and secure" team that would be able to counter some, if not most, or even all the possible opposition. Depends on how seriously you want to play and want to (over)think these things. Guess I'm pretty analytical myself nowadays.
Of course it can be all about preference, too. What Pokémon you want to use. I think there are much differences in Pokémon players in this preference vs. effectiveness continuum, if you will. I find myself being somewhere in the middle: I only want to use Pokémon that I like, but at the same time I require that they're good battlers (you know, final forms, skilled in either Attack or Sp. Attack for example, if they're not stallers or something.. stuff like that.) They must have the looks AND skills that I like!
All that said, somehow, I often prefer a Fire-type team in Gen III for some reason. Possibly because the Fiery Path (?; whatever the name is) is such a mecca of fire Pokémon that I feel convenient to catch my whole team from the same place!
Also great variety of Fire Pokémon there, great looks for everyone in my opinion! And they're relatively strong too. Plus I find it interesting to face e.g. Wallace... It's harder than usual, as opposed to me often finding the normal gameplay too easy. I don't require a whole Fire-type team per se, though, just Pokémon who all know fire moves. For years I've planned to do that team one more time and write about it...
Always loved the first Gen Water Pokémon too! Now that would be a team I'll going to do once. Already liked the type for both their graphical designs and their variety when I was a kid playing Red. Now you can find lots of variety in pretty much every type, but back then Pokémon were mainly just Electric or Fire or stuff like that (and it's actually gone to the point that I often find newer pairings like Ghost/Electric... even a bit too artificial at times). But Water was their own thing. Water/Ice of course, but Water/Fighting, too. Water/Flying, Water/Psychic, Water/Poison... I've been itching to start an all-Water team (with many secondary types) in Gen I for some time now!
Bottom line: I think it's what everyone prefers. Either maximum preference or maximum effect in battle, or anything in between. Then there may be these experiments / ideas / stuff to try themed teams such as Pokémon with same type, color, habitation... I usually go with mixed teams both because of results and what I prefer, but Gen III often is an exception since, oddly, I'm in for all-Fire(-move) teams there!