How can I minimise my opponent's chances to make use of a weak square in my position? For example, the Nimzo Indian where I don't want black to use the c4 square or the Benoni where I don't want white to use the d6 square. Is the only way to prevent this to have pieces tied down to defending that square because to me that seems like a waste.
Is the only way to prevent this to have pieces tied down to defending
that square because to me that seems like a waste.

No, it isn't the only way. There are two other better ways:

If you don't like the positions that can arise in a particular opening then don't play it. Play an opening you do like.
Normally in an opening where one side has weaknesses there is some compensation for the other player in the form of either counter weaknesses or attacking chances. Good players who choose such openings do so because they want to take advantage of those counter weaknesses and attacking chances. If they do this skilfully then their attack hits home before their opponent can take advantage of those weaknesses. But in any case they get the kind of double edged game they like.