That'd be the preferred solution, but given the existing incentives, it's almost certainly not going to happen.
It's a version of the installed-base problem: The existing House members and senators got where they are through the existing system, and it's not at all in their personal interests to make major changes.
It's also akin to the software rule that scrapping a running system and rewriting it "the right way!" is dangerous, because the running system (hacks and all) encodes a lot of hard-won knowledge about edge- and corner cases, bottlenecks, etc. In politics, it's especially true, because we have so many different players — with often-conflicting interests — who have very different ideas of what "the right way" would be. "Refactoring" is the best we can realistically hope for.
And abdicate responsibility from people we can hold accountable via elections to anonymous bureaucrats that may be knowledgable in their fields but we'd never know it.
If it's important, Congress should be willing to write it into law (or amend the Constitution?) instead of depending on a 40 year old hot fix.