While I guess that's possible depending on how it's currently implemented, it seems really unlikely.
The interface is the same as is used during character creation (or fantasia, or hiring a retainer) except that there are more features included in any of those other situations. It seems very unlikely that SE would have re-written the customization from scratch for the aesthetician and just make the UI for it look like the character creation one. They almost certainly used the system they already had, and which already has all those other customization features built into it. They just did something to disable access to several of its features when we reach it from the aesthetician. All they'd need to do is remove or modify the access-disabling rule.
From a technical perspective, this shouldn't be a major update. It should just be a decision and a minor tweak.
What about something like:
Race, clan, and gender remain exclusive to Fantasia. All other appearance settings are available from the aesthetician, but instead of a flat 1,000 gil to make changes, you pay according to the number of features changed, and perhaps even according to which features are changed. The costs would be chosen so that a single minor alteration would remain relatively cheap, but a complete makeover that leaves you looking like an entirely different character would require a fairly major investment of gil.
I think that would generally discourage the "going through 10 identities in less than a week" pattern. But it would make any individual adjustment available to those who care about it.
It would also leave Fantasia sales revenue intact from players wanting to change race, gender, or clan (and perhaps even occasionally from someone who wants a complete makeover of other features, but who tends to be more cash strapped in-game than they are IRL, so doesn't want to spend the gil for a major aesthetician makeover).
p.s. I thought your reference to "allowing us single player customization in an MMO" sounded a bit strange. Character customization is pretty rare in single player games. It's almost exclusively an MMO feature. The only single player games I can think of with anything of the kind are ones that are borrowing very heavily from an MMO style. (None of the single player Final Fantasies allow any character customization besides name and class, and not all of them allow those.)