Is the world ready for name based HTTPS vhost service? [duplicate]
No. IE (any version) running on WinXP, and Safari running on XP or older OS X won't do SNI. That's your default browsers for some of the most common platforms out.
Get a dedicated IP address. If you have a virtual private server, you have one already, and extra IPs are not expensive at most providers. If you aren't running at least a virtual private server, you have no business running an application that Must Must Must run HTTPS — cheapo shared hosting won't offer the level of security you need to ensure your data is private.
(If your concern is that you're going to be running many instances of this service under different hostname and you don't want a huge load of IP addresses, then yes, this is a problem. Usually solved by putting all the hostnames under one domain with a wildcard certificate.)
You can get a VPS with a dedicated IP at slicehost.com for $20/month. I know you said cheap, but that's not exactly expensive.
Which doesn't really answer your question. Despite the rapid evolution of apps, the net has been very resistant to infrastructure changes. Take a look at the IPv4 / IPv6 mess -- that's been going on for more than a decade. You have a worldwide installed base in the 100's of millions and none of them support (I don't think) name-based HTTPS.
This article on TechRepublic talks about SNI and includes a list of browsers that currently have support for SNI. Take a look at this list and some data from, e.g., here and make your own decision. It really depends on who you expect your clients to be.