If you take a look at the refit-Enterprise you can see that there are not many "deep" structural supports going into the ship from the warp pylons or the neck. Go-go super advanced materials
I'm not sure exactly how you would judge the "deep structural support but I'm not sure that's true.
The refit was given a wider base (the Torpedo launcher).
The neck was also reigned in more over the Secondary hull allowing for more of those perpendicular supports to be added to stiffen between the two hulls. In fact I think you could add 3 or four vertical load supporting beams directly between the saucer and the stardrive where the original ship would only allowl one because the neck protruded forward so much.
(see picture in last post)
On the refit it looks like most of the support of neck is right above the ceiling of Main Engineering.
The refit pylons are properlly mounted with a wide base but there is nowhere on the out side that I could judge how ridgid adhered they are to the ships keel.
I'll admit the very nature of the Pylons on both the refit and the original seem to imply that the material is doing the job where structure normally would because considering that there is no bracing between the two pylons at the top then it's a given that there is a lot of flexibility in them no matter what the internal structure. (and this is normal engineering failsafe, powered tech like IDF and SIF aren't a factor at this point.)
From what I learned materials do not dictate the internal supports. Like in a house. You could have aluminum beams or wood beams but you still need the beams.