The client authentication cert issued to the FQDN of the host under Local Computer>Personal>Certificates client certification path requires the PKI root cert to be deployed.
As noted, this is only true for PKI issued certs and not self-signed certs as self-signed certs don't have root authorities.
To clarify, when I look in certmgr under Local Computer>Trusted Root Certification Authorities>Certificates on a MECM client, all of the root certs are either set to <All> or to something more specific such as Time Stamping for Intended Purposes.
Ah, OK. That purpose simply calls out what purposes are valid for certs issued by that CA and have no true impact or significance.
Should the PKI deployed root cert deployed be left to <All> for intended purposes or set to something more specific such as only server and client authentication?
That's determined by the PKI's configuration as noted and is not something you should change. The purpose is metadata set when the root CAs cert is imported into the system. As noted, it's based on the certs eligible to be issued by that CA/PKI. Changing it limits systems from trusting certs issued by that PKI based on the purpose of the cert which in general probably is not desirable. Bottom line is to not change anything about the root CA's cert.