The version of authentication we included with MySQLi is a great improvement over the default user Authentication and will be the basis for the Data Bridge version of Security Assist when released. It definitely does not "totally suck" although I feel uncomfortable with that term in general.
MySQL is deprecated and will eventually be removed from PHP. I would say it is important to start migrating as soon as possible to prepare for that, but realistically that date is several years from being an issue for anyone... Let's say a version of php 6 comes out tomorrow and drops support for MySQL. It would be years before hosts updated their servers to use php 6 by default, and many more years before a php 5 version of the server wasn't available. PHP 5 came out about 10 years ago, but just about every major hosting company allows you to choose between php 4 or 5 when setting up your server, and many of them still use php 4 as the default.
So, the clock is running, but it really isn't a ticking time bomb for using MySQLi. The better reason for using MySQLi is how much cleaner the code is, how much more efficient it is to read, write, and run, and all of the work we are putting in to make it work so much better than the original Dreamweaver MySQL option.
I wouldn't say that it is "so important" to upgrade now that you shouldn't be creating sites with MySQL or that there is any risk in doing so at all. I'd say it is important to start familiarizing yourself with MySQLi and understand that it is the future. The earlier that you can adopt to that, the better, but don't lose any sleep over continuing to use MySQL when necessary. Those sites will realistically work fine for the next decade or two as long as you are ok with not being an early adopter when the latest and greatest php version is released.