While there's no shortage of progressive Christians who would love for the Catholic Church to change its teachings on all things sexual - they would see it as their successively forcing the capitulation of an old enemy - I don't think it's the laity who are clamoring for such change.
The laity who think the rules are wrong already do whatever they damn well please, and will continue to do so regardless of Church teaching. It's the progressive priests, I suspect, who really want things changed. They do not want to be associated with politically and socially unpopular positions, but being openly defiant in the Church is a good way to get defrocked and immediately lose authority, few would do even on principle. So, they hope for the next best thing: muddy the teachings so at the very least they don't have to talk about these or those sins, and can more robustly hint that they themselves reject them.
I suspect Cardinal Kasper doesn't want mercy for divorced and remarried Catholics. He wants mercy for himself. He doesn't have it in him to talk frankly about these issues, and explain why a given sin is a sin, but at the same time he wants to retain the authority he has in the church.
I doubt he is alone in that.