While I do see the thematic synergy between sorcerer and monk, and would enjoy a monk-style subclass for sorcerer, I don't think there's nearly enough power budget in the sorcerer's subclass framework to make the style of monk we're talking about here really work. And there's still way too heavy of a focus on being a caster. And Charisma is a thematically terrible core attribute for a monk.
You don't need Charisma though. If you pick defensive spells and buffs you can dump charisma to 8 and I will think you will be darn good in melee.
With the class as I said you can have 17AC in mage armor at 1st level, 20 at 4th and 21 at 8th plus 5 more for shield. You can also use SPs to quicken defensive spells like blur, blink mirror image, haste etc. so you don't lose a turn buffing. Finally you can convert slots to SPs for more flurrys so you are not constantly running out. Finally I put flurry as a stand alone bonus action, so you can do it without using an attack first. You can take any action and then flurry.
The only reason for a high Charisma is you want to play an offensive caster/gish or if you want to multiclass and either of those are moving away from the monk theme anyway.
I think together with metamagic there is plenty of power in the chassis, with the wisdom AC boost it borderlines on being OP (if you dump charisma).
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