Here is a test worth running on your own site. Your office moves. How long until the new address is live everywhere it appears? If the answer involves emailing someone and waiting, the site has a dependency in it that nobody asked for.
The dependency is usually accidental
Very few agencies set out to make themselves necessary. It happens because the fastest way to build something is to hard-code it, and the difference only shows up months later when the client wants a change and cannot make it.
The cost is rarely the invoice. It is the changes that never get made — the stale phone number, the project from two years ago still described as recent, the price that has not moved since launch. Small things, but they are what a visitor reads as neglect.
What handover should include
A content system your team can actually operate, set up around the things that genuinely change: text, images, projects, contact details. Not a page builder that lets anyone rearrange the layout, which is how a considered design decays into a noticeboard within a year.
Plus a short written handover naming what to edit where. Ours fits on one page. If it needs more than that, the system is too complicated for the job.