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> (…) not showing these connectors behind the object
The connectors are not 'behind' the connected object - they are «drawn so they begin on the edge of the attached object.»
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The routing of the connector lines is calculated and the geometry of the resulting path is stored in the SVG source as regular path data (so that other SVG renderers show the same layout, without needing to know about the special parameters Inkscape assigns to connector lines). There is no part of those lines that is 'below' or 'hidden' by the opaque object the connector is attached to.
> These connectors should be visible as the object's opacity
> is made less than 100%. Thus the visibility of the connectors
> should increase accordingly.
As mentioned, there is nothing to be shown when the object is changed to be rendered with a reduced opacity (global, fill or stroke) - I'd even say most use cases of connectors depend on the current behavior (connectors don't overlap the connected shapes):
A typical diagram may be connecting groups which consist e.g. of a text object + a surrounding rectangle (unfilled, as frame): in your scenario, the connectors would have to be rendered inside the rectangle up to its midpoint, thus overlapping the text and making the diagram possibly unreadable).
Basic example e.g. as illustrated in the manual:
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Your "cheeky way to make these connectors attach with one another" (see feature request bug #259086 and bug #492644) could also be done with clones (at least as long as bug #474881 isn't fixed ;) ).
> This is another reason, for having the visibility of connectors
> to be respectively increased as the opacity of the top
> object is decreased.
IMHO the proper way to address this issue would be to implement one of these requested features:
Bug #168748 “Connectors with manual node edits should retain their shape”
Bug #259086 “connecting connectors to connectors (wish, in order to make constrained figures)”
Bug #492644 “support to noncontinuous connectors or improvement for split connectors”