To individualize the toons into 3 categories, don't I end up losing some of the utility of each toon just due to space constraints?
I organize my team spell rotations by cast time, cooldown, and mana cost synergies. So, for example, "1" is keybound on 3 caster characters as Mage -> Fireball, Warlock -> Shadowbolt, Druid -> Starfire.

I personally don't use every spell available to each character. Its a waste of space (in macros & action bars), money (in training), and adds unnecessary complexity. For example, if you can kill a mob with one salvo of fireball x2, lightning bolt x2, why would you bind Cone of Cold for the Mages? How often would you actually use Cone of Cold in this context?

You need to accept that there are two approaches to 5 man multiboxing (true to lesser extents for smaller teams): brute force & elegance.

With the brute force approach one simply overwhelms the target with dps. As an example, watch how most people play 5 same-class teams. This is the "juggernaut". The pros here are low complexity, high dps. The con is low flexibility.

With the elegant approach, one uses the least costly but most effective "talents" (term used loosely...I'm not referring to class talent trees) across multiple classes to kill. This is the "well oiled machine". The pros here are high flexibility, decent dps. The cons are high complexity, high maintenance.

Your team is somewhere in the middle. And as everyone who has undertaken this hobby learns, the higher the complexity of mixed teams can be very challenging & frustrating in the beginning but very rewarding. The chief way to combat that complexity is to reduce the number of spells utilized and take more of a min/max approach. Refer to my example above of spell groupings. Do I use every spell available to my Mage, Warlock, Druid...no. Do I feel the "means" is elegant...yes. I'm achieving the objective with maximum output derived from minimal input and I have high flexibility in my approach.

There is absolutely nothing better/worse about either approach. The above are complete generalisations about playstyle and team makeup; you'll need to find what works for you since there are no rules that govern how you need to manage your team.