It could do plenty, with just a little imagination.
I've offered
my own version and gotten some good comment about the mechanics. It's not perfect (I'm already working on a new version) but it shows there's plenty that can be done.
Your class is pretty good. It does slide into the areas of design that I feel is reminiscent of an illusion of choice, though.
To illustrate what I mean, Radiating Confidence is made better when the Warlord uses a different feature that grants temporary hit points but in order for the Warlord to actually have that feature, they
must take the Inspiring Presence feature. This means an Ardent Soul Warlord is so highly incentivized to have Inspiring Presence that it may as well not have a choice at all.
But Inspiring Presence grants the Strike! shout a bonus. This would be okay on its own but Strike! has a pretty heavy implication that one player in your party is playing a character with a good Attack action. So the result is that Ardent Soul feels like a suboptimal subclass based on whether your other party members chose a different martial character. A whole subclass that is made better or worse based on the other player's choices gives me bad vibes.
I do like the Insight pool and the fact that it uses a more randomized resource. I would probably have the max pool a bit more understandable since at a glance I wasn't sure if the maximum was supposed to be randomly generated each fight, if the maximum was the dice maximum, or if the maximum was 2 dice.
It also has alot of moving parts that a newbie has to immediately balance around. They might get confused about when they roll the insight dice, how they expend their insight pool, when they can actually use it, etc. Its spelled out plainly but I've seen new players struggle with easier concepts. It might be, in some ways, wiser to have the insight pool be introduced at level 2 or 3.
Well good for you! As far as I'm aware you are literally the only person who thinks that a collection of things explicitly called spells, given their own chapter, that use special, specific, and exclusive mechanics, and that have distinctive interactions is just fluff.
I recognize the differences but they're so rare and minute that its hard to just say that they're so wildly different that a whole class might be needed to bridge this gap.
I can honestly say the amount of times I've been stopped from spellcasting because of their specific rules or counters (components, dispel, counter) were less than the amount of times I completed campaigns. Probably even less than 20.