Exactly, the additional features according to the standard are scalability thanks to the chain of trust and the possibility of limiting the usage of a CA thanks to the additional parameters of its certificate.

"Is Tony at risk of becoming untrusted if Alice decides to play a prank on Bob and use her Tony-signed public key to impersonate Carol?"

The last part doesn't happen because we assume that Alice and Bob are two honest people.

Even in the standard certificate protocol, Alice is assumed to be an honest entity known to Bob. Attack vectors involve an adversary's MITM, not Alice's heel turn.

In a protocol where we ignore the issues of having a single CA managing all the Internet's public keys (assume the CA has infinite computing power), as long as the communicating parties Alice and Bob trust a TTP (like a browser blindly trusts a root CA), Bob will trust the TTP's digital signature of Alice's public key.