The implicit trust you refer to is only valid for browsers, but not for 802.1X. Here, the trust comes from either explicit configuration through an MDM, GPOs, or config-files (i.e., mobileconfig on Apple devices) or TOFU (Trust on First Use). You can use a public cert for this, but it won't give your clients any trust. Just think that any holder of a public cert would be trusted. Anyone could impose a RADIUS server role. The public cert won't give you any benefit for this use case.
The cert is used between the Client and the EAP Authentication Server, which is typically the company's RADIUS server. However, with local auth, the AP takes this role.
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