I think the Household Cavalry argument is a poor one. As has been pointed out both they and the foot guards have operational roles and rotate between public duties in London and Windsor, and ops wherever they are required. In their public duties role they are "on show" all year round and although I dont know the figures but I would guess that they are at least as cost effective in
PR terms as the Red Arrows, if not more so.
Incidentally I was amused to see in the programme that
Nige 321 mentioned that the incoming colonel of the Blue and Royals (I think it was) had spent most of his career in the non-ceremonial role, to the extent that he had to learn (or re-learn) how to ride a horse before taking over his post!