An adblocker would do what you want - I guess you need to find one that will allow you to distribute block lists. For example I use uBlock Origin to block elements on web pages (including cloud links in LS) - it is possible to export / import the filter list, but I'm not sure if it's possible to script that.
edit - found this reddit article - deploying filter lists with a GPO
Not sure what happens after a LS update though.
However, I'd like to add my support for your initial suggestion that this should be an option available in LS.