I am very confused about whether the standby altimeter is required for day VFR flight: the KOEL (Kinds of Operations Equipment List) says “0” for day VFR but “1” for day IFR, while the equipment list has it as “R” (required).
You don't need the standby altimeter for VFR (day or night) but you do need it for IFR.
The Comprehensive Equipment List (section 6 in the POH) lists all the equipment required by the type certificate:
Required items or equipment for FAA certification (14 CFR Part 23 or Part 91)
But, even if a piece of equipment is required by the type certificate that doesn't mean it's required for a specific flight. The Kinds of Operations Equipment List (section 2 in the POH) lists the equipment that's required for airworthiness in day and night VFR and IFR:
identifies the equipment required to be operational for airplane airworthiness in the listed kind of operations.
14 CFR 91.7 says that the aircraft must be "in an airworthy condition" to fly, and that's what the KOEL defines.
The reason that the standby altimeter is marked as required in the Comprehensive Equipment List is that the C172S was type certified under the old part 23 rules. 23.1311 required IFR-certified aircraft that use electronic displays - like the G1000 in the NAV III - to have a standby altimeter, either mechanical or electrically isolated from the main one (emphasis mine):
For certification for Instrument Flight Rules (IFR) operations, have an independent magnetic direction indicator and either an independent secondary mechanical altimeter, airspeed indicator, and attitude instrument or an electronic display parameters for the altitude, airspeed, and attitude that are independent from the airplane's primary electrical power system
- The standby altimeter is marked as required in the Comprehensive Equipment List because it's an IFR certification requirement
- Operationally, the standby altimeter is only required for IFR flight, per the KOEL
it is required equipment under 14 CFR §§91 under the Operational Equipment List according (OEL) for the Type Certification, according to the POH. Flight operations may not be conducted without a special airworthiness waiver issued by the local FAA FSDO and only for the purposes of ferrying the airplane to a facility where the maintenance can take place. See §§91.213.