Let's say that you have put in a Cite Web via VE. If you subsequently want to add (as you forgot to) a W:Template:self published-inline there does not appear to be a way to wrap the Cite Web in a 'basic' Cite (which I take to be akin to a simple <ref></ref> tag pair) so that the template can be included in the "ref" tags as recomended. Another example ... you see that a Cite Journal is to an open access manuscript, there is not a way to insert the W:Template:Open access after the cite journal template and before the </ref> tag.
In the opposite direction, someone has put in a basic cite which could/should be a Cite Web; there is apparently no way to convert the basic to the Cite Web type, or to take the content from the basic and insert it into a Cite Web template inside the basic implementation.
All in all this boils down to there being two representations of the <ref></ref> tag pair: one as a simple tag pair (basic) and one as inseparable from the citation template being used (any of the 5 template types currently supported). My thinking is that the simplest first thing to do might be to support conversion from a supported template type to a basic wrapping the template type (cite web implemented in the basic shell, for example); this would satisfy a substantial number of use cases and would essentially be a call to "make the ref tags visible" type of action - the ref tags represented by the basic shell. Conversion from basic to a supported type could be done using the algorithm used to interpret the template type to be assigned when using the generate-from-url-or-doi method ... but there are LOTS of potential problems there.