It depends what your policy is. It seems to be somewhat nebulous. There doesn't appear to be any formal arrangement with other grand slams although, as you say, there have been swap arrangements in the past.

In America, the player development people make decisons on wild cards and you can understand why they would be interested in the red stuff at Roland Garros. Here, there's an additional policy of promoting 'British interest' to consider: a broad term if ever there were, hence the parachuting in of a three stone overweight clown into the 2017 qualifying tournament, no doubt stimulated by his centrefold appearance in Hello magazine. Can't see that as a serious, player development decision, myself. But there again, didn't Tim Henman get his OBE on some anonymous civil servant's opinion that he would 'add a touch of interest' to that particular year's list? It seems to be the British way.

Presently, we have an LTA wild card committee which makes recommendations to another committee, a Wimbledon one - which makes the actual awards. There's more committee members involved than there are wild cards. One person could do that job quite competently, any one on this forum even. There's no player base to justify multiple committees or the application of rocket science.