These are two different points.

First, the PR fallout thingy always happens. People that don't believe in Bitcoin keep moving from: "Oh no! The mempool is full, nobody will use Bitcoin if the mempool is full. Therefore Bitcoin is dead, use my shitcoin." to: "Look, there are no TXs on the mempool, not only is the 'security budget' too low, but also nobody wants to use Bitcoin, therefore Bitcoin is dead, use my shitcoin instead."

This always happens, but Bitcoin will keep proving them wrong, especially the whole stupidity of no fees=no security budget or that if compormises the security budget. Plain stupid and uninformed.

Then there are the 0 fee TX. Anyone can create those, but usually mempool rules filter them out, in order to avoid spam.

But if a miner inserts into his own mempool a Valid TXs that has zero fees, and he mines it, then so be it. The only cost would be the opportunity cost of not getting fees from another valid TX that does pay them. But if there are no other TXs, then might aswell.

In a way, this is like a bus. It's going to depart every 10 minutes regardless of how many people are waiting in the Bus Stop. If there are too many, then they are ordered by amount of fees paid. But if the bus stop is empty, and the bus is about to depart empty, might aswell take that poor homeless person, especially if he's the bus driver's brother or so.

I hope this makes sense.