AST MP management is actually better than WHM. If anyone has a right to complain about MP issues, it's the WHMs.
Let's look at some MP math.
All of AST's primary healing toolkit is a copy+paste of WHM healing toolkit, including all the same potency.
Let's use Cure/Benefic in our example.
To simplify the math, let's ignore spell speed and natural MP regen, as well as SoS and LA MP regeneration (since it will be the same for both jobs and cancel out). Let's also assume both the WHM and AST have 10000 MP each to work with (for easy %-based calculations).
Since we are comparing MP regeneration rates, let's make it a 90s test since WHM's Assize has a 90s cooldown on it and is tied to their MP regen.
Cure/Benefic have a 2.5 second recast time (otherwise known as the GCD). This is the limiting factor of how much you can spam them. In a 90s period, they can be spammed a total of 36 times assuming chain-casting. Their MP costs are different though, as most of AST's healing abilities cost less MP than both WHM and SCH even though they are the same strength.
Over a 90 second spamfest
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Cure potency = 400 x 36 = 14,400 total heal potency
Cure MP cost = 442 x 36 = 15,912 MP spent
Assize MP regen = 10% x 10000 = 1000 MP recovered
Benefic potency = 400 x 36 = 14,400 total heal potency
Benefic MP cost = 354 x 36 = 12,744 MP spent
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So what does this all mean? This means that the total MP spent for each job's primary heal spell is
12,744 for AST
14,912 for WHM
Now since Benefic II is the same as Cure II, and Helios is the same as Medica, etc etc. you're going to have the same results for all these spells too. AST will have better MP management than WHM. For the sake of argument, let's do some math for Regen and Aspected Benefic (diurnal) since they are part of the bread-n-butter kit of both jobs.
Regen lasts 21 seconds for a total potency of 1050 (since each HoT ticks in 3 second intervals).
Aspected Benefic lasts for 18 seconds for a total potency of 1030.
Over a 90 second spamfest
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4 Regens + 32 Cures (filler) = 17,000 total heal potency
4 Regens + 32 Cures = 15,420 MP spent
1 Assize = 1000 MP recovered
5 A.Benefics + 31 Benefics = 17,550 total heal potency
5 A.Benefics + 31 Benefics = 14,509 MP cost
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So in the end the AST is going to have spent 14,500 MP for 17.5k healing and the WHM will have spent 14,400 MP for 17k healing. This means that for 100 MP more, the AST is gaining 500 healing potency more. That's about an additional Benefic worth of healing for only 100 MP. Again, AST has better MP efficiency than WHM.
Now I'm not going to do this for every single spell because I don't have that kind of time, but the point I'm making is that AST MP managment is not bad. It's, in fact, better than WHM's in almost all aspects. Hell, I didn't even account for Ewer since it's RNG-based, but even in a worse-case scenario where not a single Ewer is drawn an entire fight, AST is going to be better off than WHM. Yes abilities like Divine Seal and Synestry mix things up a bit, but so do abilities like Lightspeed which reduces AST MP cost by 25% and Essential Dignity which is a free heal every 40 seconds learned at level 15 and is practically the same strength as Tetragrammaton, which is only every 60 seconds and a WHM has no access to it until level 60. But then you also have to account for Assize being a free Medica/Helios even if it's on a 90s timer. It gets complicated, but AST is not the shitty MP-hungry healer everyone makes it out to be. If anything, WHM will probably see buffs in the coming months since it offers no party utility and doesn't gain THAT much healing power in return.