You said it yourself. He would have been cheaper. The failure to acquire a viable alternative has allowed Carr and his agent to continue to bilk the Cowboys out of millions of dollars he hasn't earned.
But would he have been better? The only reason you force Carr to take a pay cut or release him is if his cap hit is keeping you from signing a player that you covet. To this point Carr's salary has done that, literally, zero times.
The Cowboys have been pretty adamant that they aren't playing in the top of the FA market and they've proven it. For some reason fans fail to acknowledge the fact (even though it's been echoed over and over again by the FO). Instead they get these pie in the sky ideas of what they WANT the Cowboys to do and and use strawman arguments like Carr as the reason the Cowboys didn't sign who THEY wanted the Cowboys to sign. "Argghhhh, if the Cowboys didn't have Carr's salary on the books they could have had the room to sign a guy that they weren't ever interested in signing to begin with" (shakes fist at the sky).
I'm with you that Carr's spot needs to be upgraded. Upgraded is the key word. If we're just going to swap parts? Nah. Robinson misses more games than he plays and his play is no upgrade. Which is why I wasn't a heart broken when he signed with Indy. But to cut a guy just for the sake of cutting a guy to possibly end up with someone that's actually worse. Not a fan.