sadly thats not the norm. Various recent studies from the EU based on real world vehicle data show that actual savings from the PHEV category are about ~20% less emissions than a pure gas version. Aka, they are just gas cars. Despite manufacturers claiming ~70-80% for emissions credits. The category is today kind of a scam, in aggregate.

It doesnt have to be - bigger battery strictly-series EREVs would likely show better numbers than the weak-ev phevs sold today.

I think it is the norm only because people never run the numbers. At least where I live gas costs me 5-10x more than electric (I live in the US, gas is cheap, but all my electric is from even cheaper wind). It wouldn't be hard to teach them to plug the car in when they are at home anywhere (many people park in a garage with an outlet - if this doesn't apply to you then PHEV doesn't make sense - you don't get enough range for your effort to find a charger)

For most in the US what makes the most sense today is one PHEV they use for long trips and towing the boat. The rest should be pure EVs, which have enough range for the typical trips and the few exceptions they just reserve the PHEV that day. As time goes on more and more chargers will be built and eventually pure EV for everything will make sense, but right not there isn't enough charging infrastructure. (You can get almost anywhere in the US, but the trip is planned around where the next charger is, not where either you feel like stopping or where the battery is low - gas stations are at nearly every exit, fast chargers 1 in 30 exits or something in that range)

One key element is whether the incentive/penalty is attached to buying the vehicle or buying the fuel.

PHEVs in a world that includes externalities in the cost of fuel will be used in EV mode more. Same vehicle different outcome.

Currently it's a mishmash with some countries penalizing electricity use while subsidizing fuel sales in lots of different little ways.

In general it's trending in the right direction though.