WordPress Network Feature

What you describe it pretty much exactly the use-case for WordPress Multisite (formerly WPMU.)

The downsides are of course that all sites are dependent on the same code and the same database so if you break one you break them all (though most of the tables are different for each site.)

Of course the upside is that you are using the same code and the same database, so you only have to maintain one set of code and one database!

P.S. There are also performance concerns for hosting too many sites on the same install (think WordPress.com), but we are talking hundreds or thousands of sites before you have to be concerned so for your use-case it’s not an issue.