'Doesn't always' doesn't discount the relationship. Human height is directly related to weight, even though there's short fat and tall skinny people. I'm not aware of any research relating location of max width vs location of max damage, and even there you have the issue of absolute width vs weaker tornadoes. The fact that the most intense damage is limited is limited to part of the total width doesn't 'ignore' anything.
Grabbing some figures from a conference presentation by Sam Emmerson, the relationship between NEXRad Vrot+TDS height and rating is clear even if there's a lot of overlap between the probability areas of ratings. The two figures are done by different statistical techniques:
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You said specifically "A lot of tornadoes that exhibit ef5 level damage look relatively “unimpressive” on radar velocities even while in close proximity, and even ones that do fail to match or surpass other TVS on weaker tornadoes". Emmerson shows that with high Vrot+TDS the chance of EF4 is very high, while when it's low, it's low:
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Condensation funnel width (the actual 'wedge') isn't the tornado's width. The tornado's the air, not the water vapour. You can't assert "I’ve never seen a case where the outer parent funnel (the wedge) produce any impressive damage by itself" and "not the actual parent funnel itself" without knowing the width of the actual funnel, which may be much smaller than the surveyed width. For example, Moore 2013:
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Photogrammetric studies of tornadoes are, unfortunately, rare these days. I'm not aware of any exploring a relationship between surveyed width and visual width, though Roger Wakimoto says he hasn't found one between visual width and damage contours, off a small sample. But to say that wedges 'have an inner violent core' you must be sure that the wedge itself
isn't the close to the size of the inner violent core you're looking for.
With respect to the vortex structure, I'm aware of the literature about how it affects intensity. I have one study (
Refan et al 2017) with a small sample but real world swirl ratio determinations are rare. Doppler studies also have problems of resolution, bias from debris centrifuging (overstates swirl ratio) and undersampling of the boundary layer. The Spencer tornado was found to have either or two-cell or multi-vortex structure and a strong translation effect. Treefall analysis of Joplin and Tuscaloosa found a surprisingly high radial (lower swirl) component (roughness potentially being important). Simply eyeballing tornadoes isn't going to do it.
If we go back to your original statement: "In reality, tornadoes
(particularly wedges) fail to develop a violent core". I think the most systematic evidence we have - the damage ratings and surveyed widths (which are not the same as Wurman's radar widths) shows 'particularly wedges' is wrong. There's hundreds of weak, narrow tornadoes for every few 'drillbits'. Whereas wedges, which as you say are rare, seem to account for a relatively higher proportion of violent damage.