There is already a plugin to remove the Site Health feature from WordPress core in version 5.2.
It is already possible to set which of the Site Health tests you would like to enable on a site using the Site Health Tool Manager plugin.
Site Health Settings
You can deselect which tests you do not want to run in the site health checker.
The MainWP Bulk Setting extension work with the Site Health Tool Manager plugin, which means you can globally set which tests you want run in the site health, checking over every connected child site.
First, you will need to install the Site Health Tool Manager plugin to all child sites you would like to. You can use this bulk setting key to add into the MainWP dashboard site, then run it on all the child sites needed.
Jetpack 7.3 also adds a number of site health tests related to Jetpack.
Jetpack: test__check_if_connected Jetpack: test__master_user_exists_on_site Jetpack: test__master_user_can_manage_options Jetpack: test__xml_parser_available Jetpack: test__outbound_http Jetpack: test__outbound_https Jetpack: test__identity_crisis Jetpack: test__wpcom_connection_test Jetpack: test__server_port_value Jetpack: test__wpcom_self_test
After you run the site health checker on any of the child sites, only the selected tests will be run.
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The site health checker feature is a useful one in WordPress core and the tests and features in it will grow over the next releases of WordPress.