Yes this Group Policy setting was the culprit for my environment as well. But the other information in this thread was very useful as well. To summarize the fix action:
The Network Security: Configure encryption types allowed for Kerberos in Group Policy needs to be configured with a checkbox to allow RC4_HMAC_MD5. The policy setting is located at Computer Configuration> Windows Settings>Security Settings>Local Policies>Security Options>Network Security: Configure encryption types allowed for Kerberos.
This should allow a Windows 10 machine to utilize the vCenter Windows session authentication checkbox to work during login to the vSphere Web Client.
The other fix actions to get the checkbox un-greyed and to get the Enhanced Authentication Plug-in to work in IE involved adding the vCenter login screen URL to the browser's Intranet Sites list. This may also need to be completed in Group Policy under Site to Zone Assignment List with a value of 1 for Intranet. Getting the Enhanced Authentication Plug-in to work in Firefox involved browsing to https://vmware-plugin:8094 and permanently storing this exception in the browser.
I'm still not able to get the Enhanced Authentication Plug-in working in Edge at this time. I am also working through untrusted certificates from the VCSA for which I have been working in the VCSA certificate manager and regenerating/reissuing certificates, downloading them, and importing them to the proper certificate stores for Windows and browsers, but no luck here yet. My certificate issue seems to be involved with the VCSA CN=<IP Address> whereas my generated certificates CN=<hostname>