Following your argument through would mean that if ATC fails to separate traffic before it comes inside the 7nm limit, the controller should shut up, and leave it to TCAS to do the job (or not).
No, the controller carries on trying to separate the traffic. If, in extremis, there comes a point where there are conflicting instructions from ATC and TCAS, TCAS is followed.
The order things happen is something like this:
1. ATC do their job and for virtually all the time get it right; but they are as human as the pilots so...
2. The two groups between themselves may, every now-and-then, trigger a STCA. This may lead to a change of plan or giving of further instructions.
3. A TCAS TA might be issued so that we can get the hosties off our laps.
4. If it gets to the point of an RA, then TCAS "controls the vertical" and ATC are informed ASAP of a deviation. Climb or descent instructions from ATC are ignored as their information is not as up-to-date as that possessed by the TCAS computers. (Amongst other reasons.)
5. When we've all missed each other, we initiate a return to our cleared levels and await further instructions from ATC...
But what, then, is your point?
My point is that TCAS is here, the installation and use of it is mandated and because of this, the way it is used has also been mandated. Until there is some real evidence that the way it is being used is wrong/dangerous, then this state of affairs will continue.
An open question: Can you point me in the direction of any hard evidence in support of the 'danger' hypothesis? Links, etc.?