The answer to this must be found in the conducted risk analysis.
Essentially, a series connection of emergency stop pushbuttons and safety gates is rather questionable,
as a safety gate is a primary safeguard for people.
The emergency stop function must also be available and functional at all times and must have priority over all other functions and work processes in all of the machine's operating modes.
Also, single errors cannot be detected
or may be concealed by such a circuit architecture, so leading to a loss of safety.