Large parties, party discipline and backroom deals are (imnsho) fundamentally at odds with a well-functioning representative democracy.
Representative democracy is meant to be a way to mitigate the problem of true democracy, which is the idea that it's easier to build a consensus among a small group than a large one and also that "the unwashed masses don't know what's actually good for them".
Bottom line is that it's impossible for 1 person to serve as a uncompromising proxy for a large group of people on multiple issues. Even if there weren't parties, there would be a point where my 95% agreement representative gets into the 5% of issues where we disagree. And no matter what, that's going to feel bad man.
Parties exist almost as a separate mechanism than government itself. They're more strongly tied to elections and voting than any specific application or creation of policy. They're about how we select our leaders, not what our leaders can do.
Unless your goal is to short circuit the process by created additional bureaucracy/difficulty in the process, it still doesn't seem like a bug. And if that is your goal, it seems more that you have a problem with the law creation/implementation and not how people's voices are being represented.
This is the problem with representative democracy; it assumes there's a good proxy for my voice, and there increasingly isn't