In the late 90's it was said that Venture Capitalists wouldn't give a dime to anyone who competed with Microsoft. Today, VC's don't want to give money to any company that competes with Google.
Google has a good product with several competitive advantages. gmail has great deliverability, you can easily join mailing lists from gmail which could exclude you if you were hosting from your_name.com. It handles large mail spools with ease because it uses parallel programming tricks. Perhaps when you boot it, it runs a quick Map/Reduce job to build an in-memory index to support all the searching and sorting you do.
I quit Thunderbird a few years ago because it just couldn't cope. It would overload, it would fail and get corrupted and I couldn't live with that. I was using Outlook at work so I switched to Windows Live Mail, which held up pretty well to the load.
With Live Mail I had two problems. First, People often couldn't read my attachments. The other was that I felt overwhelmed with the various categories of mail I was getting. Some of this was spam, but a lot of it wasn't, such as receipts when I made transactions, newsletter subscriptions, etc.
That really got me to gmail, which goes a long ways to relieve that overload.
Any product has to make decision about client-server components; I can read my gmail anywhere, and that is a big plus.
Some people imagine a massed up Outlook or Thunderbird with 64 bit addressing and designed to make the most of multicore processors and large RAM and SSD disks. The trouble is that most corporations don't give out good laptops so you can't sell this to large numbers of salespeople unless you bundle it with the hardware.
The excitement in the client world is really on the other end, you could shoehorn it into a tablet and they even have octo-core phones so maybe you can go somewhat far, but the work is going to all be in super-efficiency and managing differences between tablet platforms.
No matter what a big part of the intellectual work is some system that maintains document storage full-text index, metadata index, contact book etc. I'd like to see this subsystem reusable so that it could be used to handle other sort of document collections.
If you move the database away from the client to the server, you lose many big differentiations against gmail. (ex. You can physically destroy your mail spool if it is on your laptop, who knows who can grab it from the firm you work for. On the other hand, industrial spies can grab a laptop from out in front of you, and if you didn't encrypt the volume, they have your mail spool.)
Move the database to the "cloud" and then you are head-to-head with gmail and the advantage they have is a lot more data. It's much easier for them to know what a "discussion group", a "promotion", or a "update" is than it would be for you to do it.
Some kind of CRM functionality could be a big plus. The idea is to put structure in the communications so that there could be much more automation and also teamwork in that you can hand off the job to someone else and have people held accountable if it doesn't happen.
I think people hate CRM, Project Management and those kind of tools worse than they hate e-mail, so a "business process automation construction set" might be big success if someone can find a way to make it fun.