Can you cast banishment on yourself from a non-native plane, as a way of returning to your native plane?
From the Basic Rules, p.80:
If a spell targets a creature of your choice, you can choose yourself, unless the creature must be hostile or specifically a creature other than you. If you are in the area of effect of a spell you cast, you can target yourself.
It appears that, as long as you can see yourself, you're a legal target for banishment since it does not specify that it has to be a creature other than you.
If you were already on your own native plane and the spell successfully affected you, then at this point you would be sent to a harmless demiplane in which you would be incapacitated, immediately breaking concentration and returning you to the point at which you cast it upon yourself.
However, the incapacitation effect is not specified for creatures not on their native plane at the time of their banishment; You should be able to continue maintaining concentration for the remaining minute after sending yourself there, at which point it would be 'permanent'. (This may be a neat 'dodging' mechanic for if your environment suddenly becomes temporarily dangerous- banish yourself, and release concentration before it becomes 'permanent')
It may be worth houseruling that you have to succeed on a basic concentration check (constitution saving throw, DC 10) for shifting yourself via a method probably meant for banishing others, but that's not necessary by RAW.
If you knew the effect was coming, you could mentally choose to submit to it, this would lead to one of three general outcomes:
Natural physiological reaction. You can't control your body to the extent of deciding whether your body fights off a poison or disease. Voluntarily submit all you want, but if your body fights off lycanthropy, you do not become a lycanthrope.
Natural psychological reaction. If you decide you want to deadfall to the ground, the normal reaction is to catch yourself, but this is psychological, not physiological. With sufficient practice, is is possible to learn to deadfall, or stand and take an arrow - but healthy, sane individuals find this level of submission or self control difficult. At best, I might grant an adjustment to the saving throw if the target were blindfolded or some other appropriate limitation were employed. The player can overcome this by agreeing to be bound.
Recognition of a desirable result in a normally adverse situation. When faced with a surprise bucket of water thrown at you, it is normal to duck or dodge. However, if you know it's only water and you want the water to hit you, for instance on a hot day or if you have soap in your eyes, it is an easy thing to stand still and allow someone to splash you with a bucket of water. Worst case scenario is the referee insists on a flinch reaction and makes you roll anyway. In this case I say grant a -5 adjustment or even disadvantage. You might even allow the player to set aside proficiency and ability adjustments while insisting on a saving throw.
In the situation my character currently faces, unwillingly being in the Underdark (a demiplane off the prime material plane), away from her comfortable home (on the prime material plane), she would have no trouble standing there and taking a banishment if someone said, hold still while I cast Banishment on you. You wouldn't even have to say please.
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Need to be able to do the somatic component (so this would be useless while being grappled).
Need an item in hand that is distasteful to the target of the spell.
As per RAW, PCs cannot willingly fail their saving throw because the saving throw description says "must".
The DM gets to decide what counts as "a harmless demiplane". (If the DM is kind it will be a pocket dimension. However it could be any number of supposedly "harmless" demiplanes that the DM could choose from. A harmful plane is any plane where they cannot breath, is full of fire, is solid rock, etc, so this gives the DM many options to choose from. A harmless demiplane therefore could include the Demiplane of Shadow, aka Ravenloft, which has its own rules about visitors.)
Once there the PC is incapacitated for 1 minute.
An incapacitated creature can’t take actions or reactions, but they can maintain concentration.
If they deliberately quit concentration, they are returned to their home plane of existence. If the space they occupied is now occupied, they go to the nearest available space.
They are still incapacitated if 1 minute has not yet elapsed.