I am assuming that they are acting as a corporate travel agent. If so, they probably run some spaghetti code (which may require manual approval for difficult itineraries) to ensure compliance with the corporate travel "policy" (that's how they justify their fees) which generates the delay.

A travel agent can issue a ticket on the spot (literally), and has been able to do since since the days when you would walk into a physical store and walk out with a (paper) ticket.