Looking at the full output from wp-cli `profile hook rest_api_init –spotlight`, the worst performing callbacks are both from WooCommerce: `Automattic\WooCommerce\Admin\API\Init->rest_api_init()` and `Automattic\WooCommerce\RestApi\Server->register_rest_routes()`.
Have I tried disabling the WooCommerce plugin? Not yet (because I need its functionality, of course), but I assume it would fix it. But, WooCommerce is a really well-tested, first party product. It should work great.
How can I determine why (apparently) WooCommerce is increasing my load times by like three whole seconds?