How much access are you giving the clients? Like do they have any reporting ability at all within the normal Google Analytics interface here? https://www.google.com/analytics/
Purely from a theoretical security standpoint, you could actually do a lot of “bad things” if you wanted to with the API token that it stores internally. For example they could access all reports for all web properties. If someone was being super malicious they could simply delete all the web properties on the Google Analytics account (although I believe Google Analytics doesn’t fully commit a deletion for 30 days, so that has an “undo” option for 30 days).
You could of course prevent the web property from being changed at the user interface level, but it still would have the underlying “keys to the kingdom” being stored internally in WordPress (the token) which *probably* would be fine, but purely from a security standpoint is scary when you are turning those keys over to all clients and more or less just telling them not to do anything bad with them.
There’s the smaller issue as well where you need to somehow handle if someone picked the wrong web property initially. If the whole point is to only allow selection once, how do you allow them to change it when it was initially set as a mistake?
Do the clients have full admin access to the WordPress interface? The best solution that I can think of would be to allow certain settings (like picking the web property for reporting) to be done by users with the highest security/role, and then let lower tier users still able to view reports, but not get in and muck with the settings.
Like do you let them change other settings or do things like edit theme files?
You can find an outline of WordPress roles/permissions here: https://codex.www.ads-software.com/Roles_and_Capabilities