I've always wanted something like this but I'm not sure if the problem just applies to me or if someone else has solved this problem already.
However, you raise a good point - a nice cross-platform solution for desktop use would be a great thing to have. It's kind of odd that it's been done so well for phones, but barely touched for desktop.
One problem related will be the constant influx of 'services that may be interesting', with disparate APIs - any solution should have a good plugin system.
Obviously it's a little neckbeard-ey but once you get it setup, it's awesome to have AIM, FB, Google Chat, HipChat, Campfire (and any other Jabber account) all in one little box.
The only thing it's missing for me is iMessages support.
You can also wire up Twitter with it, but I found it too tricky to parse tweets without avatars / inline images, etc.
Sure thing!
But then I bought a MacBook, and Apple's 'Messages' app does everything I need it to. It's IM when both parties are online, and SMS otherwise.
I would also love to see something that tries to unify Reddit, Hacker News, and Google News, although I'm not sure how it could be done.
But since the chatterati think email is the spawn of old white european males, you need to get rid of "Inbox" all together. Way too emailesque.
Also, we live in the most narcissistic, shallow society ever to have sat idly on this good planet earth, so you need some combination of self, selfie, me, my, myself, you, etc.
Of course, in the selfie-sphere the major issue you will face is appearing "needy" if you respond to pings quickly or respond in a personal, non-selfish way. The proper form of communication in narcissistic society is merely post inane self-expressions in hopes of garnering hip-metrics of reblogs, retweets, likes, upvotes, and other simplistic pings.
So what you really need is an one-way orifice for self-expression that merely reports social metrics back in gamified form. Sort of like a toilet with an AI success coach built in.
The flushing metaphor has its limtis, because "flushing" makes it seem like you don't care about water conservation and other hip non-selfish, selfish things that aid your image-crafting. An "air flush" would solve the water conservation issues. So what sound would an "air flush" make? A swish, a blow? That's it.
So we should call a universal inbox in the selfie age? How about: "Blow Me"
I don't remember the names of these services now but IIRC, input.io (or something like that) was one of them. The site is dead now - didn't get any traction or funding and shut down. A couple of desktop based clients also happened but fizzled out for the same reasons.
Looks like they were quite ahead of their time. :)
I'm the kind of reading every post on Twitter and Facebook and unfollowing/muting people that post too much useless things so that would be perfect for me.
Text/IM really doesn't belong in the inbox in my opinion, because as others have stated these are in a different category of communication, with different urgency levels. IM and SMS are for when you need to get in touch instantly or near-instantly, email is for more asynchronous and/or one-way communication.
That said, IFTTT sounds like the perfect solution: https://ifttt.com
"If This Then That", or IFTTT, lets you trigger actions from events. So, if you get a Twitter mention, or an SMS, you could have it email it to you.
But they are in beta still afaik.
Niche? :)