Updating client websites on a regular basis

I hope the following question is acceptable here, as it’s half WordPress-related and half-business related.

Updating WP regularly is important for security purposes, but it can be time consuming if there are many websites to update and even more if some updates require plugin updates (and in some cases, a plugin ceases to work after WP update which potentially requires a time-consuming solution).

What is the best solution to address this ongoing problem? Should WP regular updates be charged for example? Should it be mentioned in the initial contract?

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I don’t think there’s a best solution, but whatever you decide to do, speak to the client about the issues, reach an agreement and put it in writing.
I think it’s important to discuss why we are using WordPress/theme frameworks/3rd party plugins, and what that means. The advantages: vastly reduced development time, a great community, etc., and the potential disadvantages (plugins that break).
One option is to offer six months of free support, then charge by the hour after that.
As long as the client is comfortable backing up their WP installation, then I see no reason why they can’t update the site themselves. If something goes wrong, they at least have a backup.