But club SOP does mention dead & live mag checks. Are these checks not mandatory, but up to operator / organization, that's why it's not in the POH?
The checks are effectively serving different purposes.
The "dead cut" check just after start is checking that the engine doesn't stop on one mag, showing that a mag has completely failed. Similarly if there is no drop, it would mean one mag is not being isolated by the switch which would also need further investigation. If the engine stopped during this initial check it would be a complete no go, and save you having to taxi all the way out to do power checks on one mag, then be stuck on the apron with a knackered engine. During this check you are really just checking "drop, no stop". You could easily skip this check, but then after taxiing out find you have a problem which you could've spotted much earlier.
The "drop check" during power checks is checking that each mag is functioning fully, an excessive drop would indicate a poorly performing mag, rough running could be a fowled spark plug, something which could be cleared using the mixture. This is certainly a check you should perform before each flight, and you are really looking for how much the RPM drops on each mag.
You should also do a dead cut check before shut down to make sure both mags are being isolated by the switch, otherwise you could unknowingly leave an aircraft with a live mag.