I've ruled that "The initiative of a controlled mount changes to match yours when you mount it." means that your controlled mount and you share one common turn during which you both can take actions, BA, movements, etc. but your mount is limited to the listed actions.

With this ruling your controlled mount gives up it's ability to attack in order to act on your turn, conversely you can leave it to act on it's own turn and have free reign of it's action to attack or anything else.

I can see the logic of JC's ruling, but I don't like it and I don't think it makes any sense at all.

BTW, do you have a reference for 'Jeremy Crawford thinks the controlled mount and the PC have separate turns' ?