Fit surface has no ablility to hold the edges that I could find
That is likely the case. Whenever I've seen this demo'd the resultant surfaces (a combo of using Snip Facet Body and Fit Surface) are usually enlarged and trimmed where they intersect at sharp edges. Here's a pretty detailed example on YouTube.
And another (older) video - similar approach to scanned surface data.
Another one - lots of different commands used (not Fit Surface, but Rapid Surface).
I'm finding lots of good examples on YouTube. You might end up using a combination of Reverse Engineering commands to arrive at your end goal. Let's see if the Through Points works for you.
I don't believe you're going to find an all in one solution that's going to meet every need you're expecting. Surfacing usually isn't just throwing a bunch of points at the software and everything falls right into place with surface edges meeting at 0.01 tolerances - it might not even output surfaces which might result in a successful Sew operation. I feel that you're going to be able to get larger "slab" surfaces created using points then use other tools to do the detail work (blends, transitions). You will more than likely have to use more than one command to achieve the desired results.
Fit Surface or other similar commands might just be the starting points - you might have to follow those up with Refit Face, X-Form, Match Edge or Through Curves, Through Curve Mesh or Studio Surface to get the results to be close to what the facet model represents, particularly when the real geometry is more and more complicated.
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