I only build electric instruments, but when I have to repair backs or sides, I usually use the same thickness ass the rest of the part I'm repairing. And all I've seen is always between 1.5mm and 2.5mm.
I don't see why a 4mm back wouldn't do the job (as long as you make it almost flat)... but it would be somewhat heavy, isn't it? For a top it would be too stiff and for sides maybe a bit difficult to bend.
A thinner, more flexible back can add substantially to the bass response and "fullness" of tone. If you doubt that, sit down with a good guitar, and strum some full chords holding the guitar back against your gut, then hold it so you don't touch the back at all.
That said, Martin is always a good standard to examine.
Back thickness of modern D-28 is just under 3 mm, including the finish, or .117"
I just measured a truly great 1937 D-28 that's on my bench right now - its back is 2.5 - 2.6 mm, or very close to 0.100" thick