A simpler explanation is just that they'd probably rather avoid any "Department of Time Travel" shenanigans at all cost, because that partiular element was already incredibly inconsistent within already established lore.
For example, in TNG - A Matter of Time, why didn't the Temporal Incursion Department of whatchamawhosit from the 29th century stop the 26th century historian from traveling back into the 22nd century? Then after that, why didn't they stop Berlingoff Rasmussen from stealing his ship and coming to the 24th century? Further still, why did they allow Picard to strand him in the 24th century after his time ship returned to the 22nd century? Did the time historian who was previously trapped in the 22nd century find the pod and return to the 26th century, assuming he was even still alive? If not, did agents from the 29th century travel to the 22nd century and return the pod to the 26th century, where it originated?
Yeah, pre-JJ Trek was no stanger to playing fast and loose with time.