I think everybody's missing the forest for the trees. The problem isn't that a grappled character remains grappled. The problem is the shut-down nature of a grapple. A grappled character can't cast most of their spells, probably can't attack with their weapons, and pretty much can't do anything without making a grapple check.
For a fix, just change assumptions about what being grappled means. Assume that a caster can easily work an arm free for somatic and material components. Assume that a fighter can pull back with his sword arm enough to whack an enemy with his sword. Assign an attack penalty, sure, but let them continue acting. As long as a PC can still do things, not being able to escape from the grapple is frustrating without being the end of the encounter for them.
For a fix, just change assumptions about what being grappled means. Assume that a caster can easily work an arm free for somatic and material components. Assume that a fighter can pull back with his sword arm enough to whack an enemy with his sword. Assign an attack penalty, sure, but let them continue acting. As long as a PC can still do things, not being able to escape from the grapple is frustrating without being the end of the encounter for them.