Figuring out how, and how much, to pay, and then fumbling with cash and change or whatever, during the fairly stressful experience of boarding, is something of a barrier to using transit. So removing the fare payment entirely removes that barrier. But, that's gotten a lot easier with support for paying fares in apps, so I think it's a lot less of an issue now than it was ten years ago. I used to be in favor of free fares, mostly because it'd make using transit less intimidating for newbies. But I'm on the fence now.
As you say, it has gotten a lot easier, and nyc is the easiest out of the systems I've used recently. You tap your phone, any credit card or a card you get with cash (replacement for metrocard), and the gate opens while they take your money. 12 taps and you're not charged anymore for the week.
