Some Practical Implications

See Theorizing.

The base timeline cannot be changed.

There is no need for a Time Patrol to prevent causality violations in the base timeline.

In that timeline, one theory of "time travel" might be that it is an elaborate form of suicide and should therefore be discouraged or even prevented for that reason. However, once a time traveller has departed, nothing further can be done.

Of course we know that the first departures into the past coincided with the outbreak of a civilization-destroying nuclear war so maybe that is the end of the matter in any case?

Is there a cosmic evolutionary process whereby intelligence that is about to make itself extinct in one timeline creates and escapes into an alternative timeline?

Fly in the ointment: Fuchs, the inventor of the temporal displacement apparatus, has a real, not duplicate, dolabra (Roman soldier's entrenching tool). Has his apparatus reached into the past and extracted this tool? Or has someone travelled into the past and brought the tool with him on returning to the present? - thus upsetting my carefully constructed theory that all "time travel" is into an alternative timeline? Time travel is a very difficult concept to discuss consistently. 

Returning to my theory for the time being, if time travel is invented later in the alternative timeline, then that timeline becomes the base timeline for a second alternative timeline. And so on.