Is "Month" leve mandatory for a Time Dimension?

One of my colleagues suggested to have only "Year" and "Day" level for a Time Dimension to improve the cube performance for one of our projects. His idea is that if the customer wants a Month level, he/she can query from the underlying data mart directly. I don't agree with it. Please advise whether a "Month" level could be omitted in a Time Dimension.

You could drop anything you want. Question is, does it make sense?

How does that improve performance? There are just as many rows in the dimension.

It is unlikely to make any difference to performance and having to go to two different places (cube and mart) for similar queries doesn't make sense (or a great user experience)