The benefits go further than Club access. The Presidential Plus card grants waivers for the 4-segments and PQD qualifications, whereas the Club Card earns 1.5 miles/dollar spent. So, one may want to have the PP card, but not use it for spend, instead using the Club card for that.
I understand the benefit of having the PPMC, it has a lot more benefits than the Club Card. But instead of having both, wouldn't it make more sense to have a Sapphire Preferred (or Ink) and just dump the points where needed? Or a card that has a 2% cashback? (This can surely be debated ad nauseum, but I'm still having trouble working out the math behind it to make it advantageous.)