The designs for this task show a rich-text editing feature for template parameters, but VisualEditor doesn't even have that yet, because it's hard. For example, you assume that parameters that are page names or image names will be editable as links/images, but that's probably only the case if the template call looks like {{foo|link=[[Bar]]|image=[[File:Baz.png]]}} as opposed to {{foo|link=Bar|image=Baz.png}}. More generally, templates can do insane things with their parameters, like not rendering them (yes/no params for example are not rendered directly), rendering them conditionally, or rendering a manipulated version of them. Template wikitext is basically a programming language, and Lua is an actual programming language, so anything is possible.

For infoboxes it's generally the case that parameters are rendered exactly as they are input, but this assumption breaks down in more complex cases. That wouldn't be much of a problem if you could tell which parameters are safe/suitable for rich-text editing and which aren't, but without special TemplateData or Parsoid support (or maybe both) I don't think you can.

In T139332#2674763, @Catrope wrote:

For example, you assume that parameters that are page names or image names will be editable as links/images, but that's probably only the case if the template call looks like {{foo|link=[[Bar]]|image=[[File:Baz.png]]}} as opposed to {{foo|link=Bar|image=Baz.png}}.

If the template is like the later, it has two parameters that are filled with two pieces of text, and that is what will be represented in the editor. There are no plans to do any kind of magic to figure out what text may be interpreted as. Rendering it as rich text would make a difference only when the content has wiki markup.

I recreated below how the templates could be translated in both cases:

{{foo|link=[[Bar]]|image=[[File:Baz.png]]}}

{{foo|link=Bar|image=Baz.png}}

In the second case, I agree you don't get the benefits of visualising the result (as it happens with the current template editor), but you still have the parameters aligned to facilitate the back and forth of translation, the regular tools for editing available as with any regular paragraph if needed (e.g., automatic translation in case you needed to translate "bar" into Spanish), and the ability to comfortably write more than one line of content. I'm not sure which is the problem in this case.

For translating we don't need to support all kinds of templates (since currently very few are supported), but I have not found an example that didn't fit in the proposed model (one of the most challenging parts is the use of templates as parameters for other templates, but I think they can work in the current model and will document that in T145857). If anyone can point to a template in a Wikipedia page that seems specially complex, I can try to represent it with the proposed model to see where it falls short.

would suggest option for wikidata infoboxes where available
for example
https://en.wikipedia.org/wiki/Template:Infobox_person/Wikidata
and
https://fr.wikipedia.org/wiki/Mod%C3%A8le:Infobox_Biographie2