Then you may as well ask the world to call China "Zhongguo", India "Bharata" and Japan "Nihon/Nippon"

Living in Nusantara itself, I've actually never read/heard any public figure from Malaysia or Indonesia use the term in speeches or statements. Nusantara isn't that common a term anymore, even in the Archipelago itself.
The Malay aspect of "Malay Archipelago" derives from the term "Malay race" which was incorrectly coined by a couple of white guys in colonial times. Since the Western world takes no interest in historical correctness in the Eastern world, that label stuck and now there is a misconception that this term is completely acceptable.
It is a term that Westerners use to simplify the region but it is a very lazy term.
Malay race would make sense if the various island cultures were overwhelmingly similar as Malays. But it is not. For example, there is the Javanese race and history, which is completely and utterly distinct, yet in the Western world Java gets lumped in under "Malay archipelago", "Malay language", "Malay race", etc.
A much more acceptable term then, if Westerners find it so necessary to simplify the people, is Austronesian. Makes way more sense. But better still to specify.
As for the name of the archipelago itself? Again, specify. If you are referring to Indonesia, say Indonesian archipelago. Malaysia (and a few specific parts of Indonesia derived from Malay culture)? Say Malay Peninsula. Philippines? Philippine Archipelago.
Don't want to call it Nusantara? Fine, but don't call it Malay Archipelago.
Remember when people called the entire area East Indies? That is the equivalent of calling it Malay Archipelago today, albeit balanced from a modern perpective
I say this as an Indonesian who has studied the area far too long to accept outdated terms