Overriding a core block in 5.7 in my theme package doesn't work

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I'm running 5.7.5.8, which at the time of writing is the current release.

I've styled the social_links plugin for my theme, and if I put it in my theme package as a custom template like this, it works:

my_theme_package/blocks/social_links/templates/custom_template/[view.php, etc.]

However, I want to override the default view without a custom template so it works without specifying it, as I believe it should, like this:

my_theme_package/blocks/social_links/[view.php, etc.]

This does not work, however. I've cleared cache and refreshed, etc. I know I could override it in the core application directory, but I'd really prefer this just be part of my theme package.

Is this not possible?