Developing a custom solution feels always fast, because you are actively writing code yourself.
On the other hand, when using Joomla or Wordpress, you need to learn existing system and you spend more time on the learning side of the things.
If the CMS is not specialized (video, government documents, etc.) it rarely pays off to write custom stuff: in the end you need to write much more code, though that development might feel to have fast pace. PHP CMSes are well productized and the benefits of picking one outweight the benefits of maintaining large codebase written by a single person (you). With open source CMS you can draw resources on much larger pool.
Also it is your customer benefit to base the codebase on well-known product for the cases where you might not be available. It would not be honest business if you leave out telling the benefits of open source for your customer.