They weren't handcuffed, they chose to do it that way. It's like if you have 50k, and you use it to buy 1 car. Or, you can put 10k down five times and have five cars. Same money spent, four more cars. Dallas chooses the 1 car. Then says look, we have no space.
We'll call this one car Dak. Anyone that is against giving him an extension can't complain about not signing free agents. Signing Dak would create (short term) a lot of cap room. Signing Lamb would create some cap room. Signing Parsons would cost cap space.