There's already an industry standard for that - Avid Sibelius. If you're composing in a traditional manner, a DAW probably isn't the right tool.
Classical notation was fantastic for use with pen & paper when music was much more conservative and on-the-beat. But we have computers now. We can come up with something better — whether it's software like StaffPad[1] as a first step or something even farther removed from classical paradigms.
I've also written a bit about this in my blog[2]. Frustration with classical notation was one of the reasons why I worked on my own "anti-DAW" music app. (Though it's a somewhat less ambitious project than Helio.)
[1]: http://staffpad.net
[2]: http://beta-blog.archagon.net/2016/02/05/composers-sketchpad...
Sibelius has fairly good support for swing, shuffle and irregular meter. It has natively supported quartertones since version 6; plugins provide good support for alternative tunings and microtonal composition. Classical notation can get clumsy if you're doing really weird things, but "really weird" is a higher bar than you'd expect.
If you're using timbre as a fundamental expressive element, then a DAW is probably the right tool. At present, we have no useful system for notating synthetic timbres.
Other new tools like Staffpad are amazing, but they serve a somewhat different market.