There is no one-size-fits-all solution. Having the option of the Citibank benefits or Amex FHR does not preclude making other bookings through a TA.

Virtuoso etc. is usually the best way to go, but on the other hand the Citibank program includes some hotels (mostly four star) that are not Virtuoso or FHR.

As you note, the card "pays for itself," so it's worth having even if you continue to book through your TA, which you should do IMHO.

TAs do want your business, especially if the booking is relatively substantial and is not overly complicated.