Only the number of special attacks is limited

Note the last paragraph of the Unwavering Mark feature (XGtE, p. 30):

Regardless of the number of creatures you mark, you can make this special attack a number of times equal to your Strength modifier (minimum of once), and you regain all expended uses of it when you finish a long rest.

This means that the mark can be applied any number of times but the special attack that you make is limited by your Strength modifier. So, you are correct in your assessment that the mark remains useful even if you have no more special attacks left to use, because this part of the effect still happens:

While it is within 5 feet of you, a creature marked by you has disadvantage on any attack roll that doesn’t target you.