And when has he done that?

Almost always. There are always disagreements about what the laws require. When that happens, those affected by those disagreements have access to the courts. Every President ends up doing things that end up being overturned in court at some point. Trump lost cases in court, Biden has lost cases in court - whoever the next twenty Presidents are, they will end up doing things they claim are legal, but which end up being overturned in court.

When looking at what policy options are available to the President, we generally are talking about what options are within his legal authority, as will likely be determined by the courts.

In this situation, the President's authority as Commander-in-Chief in no way would relieve him from the requirement to follow the asylum processes that have been set out by Congress. He has to follow those laws. If he doesn't, the courts will order him to do so - and the fact that he is also the CIC will not change that.