Rather than your question (which Sten has already answered well), let me reply to one of your comments under Sten's answer, since I think that's where the core of your misunderstanding lies:
In this scenario [where Moon's orbital period = Moon's rotational period = Earth's rotational period = 24 h], the Moon's orbital period is the same with the Earth's rotational period. So the Moon will be only visible to a certain region of Earth. Well, the Moon also rotates every 24 hours. So people of that certain region can see both sides of the Moon (12 hours one side, and another 12 hours the other side)
No, that's not what would happen in your scenario. It is, however, what would happen if the Moon did not rotate at all.
As it happens, Wikipedia's article on tidal locking already has an excellent animation illustrating this, so I'll just borrow it:
Animation by Wikipedia user Stigmatella aurantiaca, used under the CC By-SA 3.0 license.
On the left, you can see the Moon orbiting the Earth (drawn as just a circle, and obviously not to scale) while also rotating at the same rate as it moves around the Earth, so that it completes one orbit around the Earth in the same time as it completes one rotation around its own axis — just as it (on average, neglecting libration) does in reality, and as it would also do in your scenario. You can clearly see that this results in the same side of the Moon always pointing towards the Earth.
On the right, meanwhile, is what would happen if the Moon did not rotate at all while still orbiting the Earth. In that case the side of the Moon facing the Earth does change: the Moon doesn't rotate, but it moves around the Earth, so that people watching it from the Earth see it from different directions.
(The Earth itself is drawn as just a featureless circle in this animation, so you'll have to imagine its rotation. But if you imagine it rotating at the same rate as the Moon in the left animation, so that the same side of the Earth always points towards the Moon, then you'll have exactly the mutual tidal locking scenario you envisioned.)
For an alternative visualization, get a friend to help you and have them stand in one spot while you walk a full circle around them, with both of you looking each other in the eyes all the time. Obviously your friend will have to make a full 360° turn in order to maintain eye contact with you as you walk around them — but so will you! If you started the turn e.g. with your friend on your west side and went clockwise, then you'd end up looking first west, then north (after walking 90° around your friend), then east (after 180°), then south (after 270°) and finally west again (after walking a full 360° circle).
Or, if staring your friend in the eyes while walking around them feels too creepy and awkward, just hold hands with them instead. Or just hold your hand against a tree or a light pole while walking around it.
In any case, any time you walk a circle around something while keeping it on the same side of you, you'll inevitably end up making a 360° turn. And conversely, any time you walk around something and turn a full 360° at the same time, the same side of your body will always face the thing you walk around (at least on average).
Meanwhile, if your try to walk around your friend (or a signpost) without turning at all, and initially face towards them, you'll find that after walking 180° around them you now have you back towards them instead. (And if you practice your footwork until you can do the full circle like that smoothly without stumbling, you'll now know how to do a basic do-si-do and be one step closer to perfecting your folk dancing skills. Congratulations.)