ZyroMane: The protector/medic combo in Etrain Odyssey is just bad. Too much defense is just bad, and that works both ways.
Worth noting that, in my most recent EO1 playthrough (a long time ago):
* I did not have a medic; healing was handled by a protector (early) and a troubadour (after learning that healing song, which is one of my favorite EO1 skills, but unfortunately absent in EO2 (my least favorite of that trilogy))
* I did have a protector (though I don't remember if I kept them the entire game), but didn't actually use the defensive skills IIRC. (Or, at least, I *think* I did.) I think I had a Dark Hunter, who can self heal with drain attacks (but otherwise wasn't that useful IIRC).
* One thing is that I also avoided relying on items for healing.
* There were some times when I'd intentionally prolong a battle in order to heal. (Worth noting that I actually *like* this style of gameplay sometimes.)
On the other hand, too much offense is also bad, particularly since you don't even get to see what the bosses are capable of. Like, in EO2, a full offensive strategy, perhaps using that one Hexer skill that does huge damage at low HP, can kill bosses before they have a chance to do much. What really hurts, however, is how the game actively punishes defensive strategies (which is one thing that frustrated me in this game, though postgame wasn's as bad about this).
(Worth noting that, while I like EO1's gameplay, there is one plot element tat bothers me, and I consider it to be in poor taste. In fact, it's bad enough that the game needs a content warning, as it could very well be triggering to anyone from an indigenous population.)
ZyroMane: I've always been more attracted to the abstract thought in Mathematics than just pure figures or arithmetic. The theory of arithmetic is much more interesting than mere raw computations, for me. Makes sense that Real Analysis was my best subject. I did, however, really enjoy my studies on Topology and Differential Geometry as well. And that's the thing about the trinity. The damage dealer gets huge numbers. The healer tops off bars. The tank doesn't get as obvious a picture that they're doing well, but they feel it. Of course, that lowers the appeal of the role. And in PvP, they often tilt both teams' healers. Sorry about that.
My favorite part of topology was the counter-examples. You think you have a mental model of how things work, but then there's some bizarre counter-example that proves it wrong, and two definitions you *thought* were equivalent actually are not. My project was in chaotic dynamics, but it just so happens that number theory is still one of my favorite subjects. (I recently worked out how you can divide by 3 using only additions, subtractions, bit shifting and operations, and constant multiplication (which is just a fixed length bunch of the other operations).
I happen to really like the dynamics of healing. This can, for example, be working out which healing abilities are more efficient (important in high attrition games, but not in low attrition), and when that situation might vary (single versus multi target healing). There are other variables, like the stat that's used (see White Wind in Final Fantasy 5-7 for an example of unusual stat dependence for a healing ability), and the speed with which the action is performed.
For example, for my CRPG I've thought of a couple healing abilities:
* One is a medium strength healing ability. This can get quite good if you raise the stat high enough, but it's not the most powerful, and it's only single target. However, this particular ability is fast; it always goes first in the round. This is useful if you need to heal a character who's severely injured during combat before the enemy can finish them off.
* Another is a weak party-wide heal. It's cheap to use, but in addition to being weak, it is slow, always being used at the end of the round. This is the sort of healing ability that might be used as a preventative measure, perhaps used every round of a boss fight. To make things more interesting, I'm thinking that this healing ability may use a different stat than the one above, so you have different characters likely taking on different healing roles.