We're a YC company (www.post.fm) working on one of those ideas - email. We've encountered lots of headwinds as PG mentions, and we've managed to stay strong to our beliefs by keeping the team small and focused, and using our product ourselves to constantly remind us that what we're working on is better than Gmail.
It's not been easy admittedly, we didn't come up with some small idea that could grow into an email replacement over time, or some add-on to gmail to give us early traction, etc. We focused on replacing Gmail from day one. And that's no small feat, cause who wants to use a minimum viable email service?
We also realize it's a huge bet, and we may be wrong. But at least we're building something for ourselves, so we can't be too wrong, and that thought keeps us going.
Can't say I agree with "Email was not designed to be used the way we use it now. Email is not a messaging protocol. It's a todo list."
Email was designed to be the electronic version of a letter - an async messaging channel. Not some to-do list protocol. But with increased volumes managing all that mail became difficult (I'm sure celebrities still struggle to catch up with physical mail). That's the problem we want to solve, by letting algorithms and better user interfaces help you manage your mail.
A to-do list is something different in my view, but naturally closely related (and should be part of the same application). A piece of mail often prompts you to create an associated to-do item, but today this functionality isn't integrated so we rarely bother.
Sure IM, Twitter, and To-Do list apps chip away at some of email's use cases, just like instagram is doing with facebook, but we're confident that email can be just as good if done right.
Now I just have to finish it and avoid thinking about my idea for the google-search-killer that would be oh-so-easy to try out ;)