Might make some rules wording easier if limitations are imposed during the Mythos phase. 'Next turn' rules writing is trickier than 'This turn'.
Just to be clear, I think players take "turns" during the "Investigation Phase" only. With regard to this discussion I think you mean "next round" or "this round." Rounds begin with the Mythos Phase (except for the first round) and end after Upkeep is complete.
OP: It is somewhat true that skipping Mythos on the first round means that it is similar to what we have seen before in, say, Eldritch Horror. But more importantly the final step of the Upkeep phase marks the end of card effects that last until the end of the round. In the Rules Reference under the Upkeep section it reads:
4.6 Upkeep phase ends.
This step formalizes the end of the upkeep phase.
As the upkeep phase is the final phase in the round, this
step also formalizes the end of the round. Any active “until
the end of the round” lasting effects expire at this time.
After this step is complete, play proceeds to the beginning
of the mythos phase of the next game round.
This ensures that the effect ends at the end of Upkeep and before Mythos. This is likely a key timing point for the mechanisms of the game.