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Custom web parts (spfx) are not available from subsites without installing the add-in. #518
Today you have available both ALM API ( https://docs.microsoft.com/en-us/sharepoint/dev/apis/alm-api-for-spfx-add-ins ) and tenant-scope deployment.
If you want to install spfx web parts to subsites for on-prem too please take a look at my blog post -> https://rasper87.wordpress.com/2018/04/26/provision-spfx-web-parts-to-classic-sites-part-3-install-spfx-web-part-to-sharepoint-site-web/