That way of thinking ignores several facts, not the least of which is that paying sometimes exorbitant prices to see a show does not guarantee quality of a production. Why then should we feel that a free production can not be also a fantastic one?
Most of the production I've been in have been either pay what you can or low cost. Not all of them, I must admit, were fine productions, but the majority were. That's because the quality came not from the money spent and money made on the show, but on how much I and the rest of the cast and crew wanted to do well. When their is no financial incentive you can bet the money you are not paying for a ticket that people are in the show because they want to be, and that matters.
Quality is a decision to work hard, nothing more. When that decision is made by everyone involved in a show, and all of the same people enjoy one another's company the quality of every aspect of the production increases. That chemistry and that pride can't help but show through to an audience. Audiences, whether they realize or not, respond better to shows where the cast and crew enjoy what they're doing and enjoy one another.
This is especially true with audiences who don't come to the theater o a regular basis. Audiences who in some location may not be able to afford the average price of a ticket. And since free shows would allow more people to enjoy a production, the better the experience is for all involved. It's cyclical.
Some may argue that those who see shows for free have made no investment, and hence have no incentive to behave well or to respect the actors. That may be true for a certain element, I concede, but then again such people are not likely to show respect for something even if they did make a small investment in same. A decent person either respects someone's work, or they do not. With few exceptions I've not in my years as an actor detected a noticeable drop off in how receptive or well-behaved an audience is when admission is free or low cost.
In either case, that speaks to the quality of the audience, and not the quality of the performances.
The piece goes on to mention a few professional companies offering free performances for limited time. That's nice, but I don't think it's the same as producing a show that is free from the start. If an otherwise expensive company throws a few bones out there, people are not likely to assume that there is a poor quality free show in the offing. They will merely take note of the fact that the company is giving away seat for a few days.
We see many different types of art for free, in museums and galleries. Our parks host free concerts in summer time on a regular basis. The fear of poor quality in those cases doesn't seem nearly as strong as it is for free theater. Perhaps it is a side effect of theater as a whole being beyond the means of so many people for so long, I don't know. I do know that those who skip theater because they aren't paying much, if anything to see it are depriving themselves of some wonderful experiences. If it's bad, then of course they haven't lost anything, and can leave. But if it's wonderful, (and if often is) they've received for more than a free place to sit in a dark room for a few hours; they've had their humanity confirmed and might just feel a bit less lonely in the world after the show.
Sounds like a decent trade in for nothing.