TLS terminating LBs/WAFs/<things> that cant authenticate the client cert or pass the public key through to something that can, dealing with key/cert expiry, nobody to run the PKI infra with any interest managing identities of things that aren't AD computers, you name it.
Now somebody needs to manage the resulting PKI.
Even what looks like the no effort case, where you punt to the Web PKI and have all the clients use Web PKI certs (ie client1.example.com needs a cert with SAN dnsName client1.example.com like a web server would have but making sure the EKU for client auth is asserted) means now you have to either keep pace with us, or risk an impedance mismatch if our policies change in a way you're not OK with.
If you use one or more private CAs there's a tension between on the one hand the convenience of it not being your problem, and on the other hand the risk that it turns out you were just engaged in theatre and there's, for example, an unsecured SCEP server that will happily give any adversary with network access an authorised certificate with whatever identity they ask for...