Not a Bluehost employee or customer myself, but just weighing in with some helpful context here.
Upgrading MySQL on a shared server environment is much more complicated than just flipping a switch, like upgrading WordPress. Even with PHP, hosting providers can offer multiple versions on the same server and allow you the customer to choose which version is used by your site.
MySQL is very different, it can only exist as one version on the server, which means that an upgrade to MySQL is going to affect every single site on the server, not just yours, and not everyone’s site is going to be compatible with the latest and greatest MySQL (not everyone is lucky enough to run WordPress).
This is why managing your own server via VPS/Cloud/Dedicated is often recommended to folks who want the latest and greatest ASAP. If your site is the only site on the server, and it can support the latest and greatest MySQL, then there’s no barrier to upgrade.
So, just keep in mind that while most decent shared hosting providers do their best to pursue the latest and greatest as quickly as possible, they have to do so in a manner that will not leave the rest of their paying customers in the dust.
If always being on the latest and greatest as soon as possible is very important to you, I highly recommend considering some sort of VPS/Cloud/Dedicated hosting, so that you can be in control of that.
And, please keep in mind that, while the recommended version of MySQL is 5.6, WordPress only requires at least MySQL 5.0: https://www.ads-software.com/about/requirements/