That will work as long as all of the devices do not share a common...
Am I misunderstanding something, or was this just a typo?
Thanks for confiming or elaborating!
Usually someone would use the term "ground" instead of "common" but it is more properly refereed to as a common.
By replacing all of the separate floating power supplies with one, you are creating a common between all of the powered devices. This will work as long as the devices are not otherwise connected in a way which creates a different common.
Usually this is not a problem because most devices these days use a negative ground (1) but there are exceptions sometimes like if the designer included a reverse protection diode in the negative side, included a full bridge rectifier so that a DC or AC power input could be used, or chose to regulate the negative side of the power input for some reason instead of the positive side. If everything is connected using Ethernet, then it is irrelevant because Ethernet provides galvanic isolation.
So it will most likely work fine but if there is a problem, sharing common through some other path is likely the issue.
(1) But this is not a guarantee since if the devices uses a negative ground and have some other galvanic connection between them, this creates a ground loop which may be problematical. Again, if only Ethernet connections are made between devices, this is irrelevant because Ethernet provides galvanic isolation. This is *why* Ethernet provides galvanic isolation.