But in airspace where TCAS carriage is not mandatory, the majority of other aircraft have no way of detecting you.
Of course they do. You can buy a number of simple transponder detectors for a few hundred quid. As the carriage of transponders becomes more widespread, the sophistication of such devices will increase and the price may fall.
Maybe we should have a regulation for all Commercial flights operating outside CAS to have airborne radar fitted - it is proven technology, it would be paid for by the beneficiaries,
They do have radar fitted. It's called TCAS. But it's a secondary radar, and it needs cooperation from the other aircraft flying in the space. Suggesting that they carry primary radar is analogous to suggesting that they should carry massive searchlights capable off lighting up other aircraft in their path to save the others from having to display lights.