it requires me to enter a recurrence interval.
Obviously :-) The trigger does not work in push but in pull
The email server does not push anything to the logic apps when a new email arrives (this is push approach). It is up to the Logic app side to connect the email server and check if a new email arrives (this is pull approach). In other world it is not really a real time trigger which executed when a new email arrives but a logical trigger which check the server every X time. This parameter allow you to configure the interval time between checking for new email.
This is inconsistent with the online documentation, which does not mention anything about a recurrence interval
Seems like you sue the word inconsistent wrongly. Not telling someone the entire true does not make it a lie (even if it might be worse) and Not presenting something does not make it inconsistent. If you see two points which present different information then please provide it since this is the meaning of inconsistent (information in one place inconsistent with the information in another place)
Is there a reason it is forcing me to enter a recurrence interval, instead of just triggering whenever an email arrives?
And how do your think the logic app will know that a new email arrived ?!?
The Logic app cannot guess when email arrived and you are not developing anything in the email server side - there is no trigger in the email server side, then the only option the logic apps know that an email arrived is by checking it and it cannot check in stream 100% of the time. The logic apps check for new email every x time