There are some great answers already available, but I wanted to give you another perspective. I've been developing Wordpress and Joomla sites for years, and I do appreciate Wordpress quite a bit. The downside, though, is that Wordpress is a dog. It is slow. Since you are partial to it, I'll respond about it specifically.
Sure there are plugins that enable caching, but the real truth is that for every page viewed by a user, it requires the server accessing hundreds of files which then require even more memory to process. Even the caching plugins don't hold a candle to a custom developed system when it comes to speed.
What I've done for my clients is to give them the best of both worlds. I develop a custom frontend which does not use anything from Wordpress, except the database. This gives me full control and I don't have to worry about their framework or updates (unless there is a database change). And the client still can use the Wordpress administration section as normal (except some plugins need to be converted).
If you are planning to have a large number of visitors, it might be the best route, or you risk having your server crash when someone submits a link to reddit or the like. The downside is that type of development is costly.
I can't provide samples of what my clients sites are, but I certainly have seen Wordpress being used for Rand Paul:
The page source tells us they use WP-Super-Cache, which helps a ton to speed things up. If you don't have a large budget, Wordpress combined with WP-Super-Cache would work too and save you the need for a custom frontend.