Another team doesn't want a bad player either. Teams can give said player a regimen, they can place them in the care of third party coaches and trainers to work on weaknesses and allow them to study the playbook.
Dawson got beat out by JC Jackson... period, and the Pats didn't want to give up on him completely so he magically got injured and tried again next year... he still wasn't good enough so they traded him to Denver to recoup some draft capital. We'll have to agree to disagree, you believe teams have a moral obligation to follow the rules to a tee... some like real life.