I think AST lacking the MP regen that WHM does is an easier argument to make when it comes to balance.

Yes, WHMs spells cost more, but that's more than offset by Freecure over the course of a usual fight. I think the actual math puts it in favor of a WHM overall.

If we're making direct comparisons, then LA = SoS, which leaves the only realistic answer to Assize to be some combination of Ewer, CO, and Lightspeed (though, Assize is a potent MP tool not just because it restores MP, but because it is 1000+ MP worth of healing for free, but I'll ignore that for now), which compared to a WHM, mostly require the AST to give some of their raid utility up (not saying that choice is a bad thing, but it makes MP more dynamic and strategic for AST).

On paper, for now, it probably works out, but this really stems back to my main issue with a lot of theorycrafting when it comes to Astrologian. It's very easy to look at the math and say "well look you only need ___ number of ___ to match (other job's) _____" for any given fight! But if your signal that two classes are perfectly balanced is that if one gets a certain amount of an RNG mechanic on multiple fronts to match another's MP/mitigation/damage, then it's not truly a fair comparison within FFXIV's raid scene.
We all know that FFXIV raids are heavily scripted, and basically 100% reliable in terms of mechanics. If we saw more encounters that highlighted adaptability in gameplay and spell choice, I doubt we'd see as many ASTs feeling slighted, but as it is, the RNG of cards doesn't really mesh well with the way FFXIV's raids are designed.

But the above junk is really just my opinion. If you want a concrete, pretty much irrefutable concern regarding Astrologian MP, it's that going forward they are the only healer whose MP regen abilities don't scale with Piety in any sort of way. Every point of piety on gear will create a widening gap in MP management ability between AST and the other healers. It could end up not being an issue, but design-wise it's definitely a glaring potential issue.