This is going to be short, but the general point is that, yes, of the scripts you have mentioned, there are in fact fair justification for considering them as derivative from a single parent script, at least through influences if not direct development. Each of these can be linked back to Proto-Sinaitic which it in turn derived from hieroglyphs. Does that mean that the connections are certain and free from any potential criticism? No, but we can still be fairly certain of their relatedness.

There are of course detractors, such as is found in the other comment about hangeul. However this comment is supported neither by the history of the script nor by the governing bodies which would have something to gain by giving such support, and as such can be ignored with reasonable degrees of confidence. There's simply no reason to believe hangeul was not based on 'Phags-pa.

Realistically, based on the currently accepted views within the field regarding the development of orthographic systems, there's absolutely no reason to believe the different writing systems about which you are asking were not based ultimately on a single common system, however unintuitive that may seem.