Exchanging keys via third party
Yes, if you are using 3rd party key exchange, the 3rd party can read the messages. If that is not the security feature you want, use something else. There are many legitimate scenarios where users are fine with trusting the third party, however. For example, a system setup by my employer to allow encrypted chat between myself and our clients. My employer has legitimate reasons to want to be able to access those messages if necessary and so would want to set it up with (possibly) third party key exchange. I, as an employee, might be fine with that as I would be conducting official company business using the system.

Older protocols might have done this before public-key crypto was invented in order to keep key management reasonable.