What is the benefit of 'voluntary page charges'?
The benefits of "voluntary" page charges are much the same as for "mandatory" page charges - you are paying them in order to support publication of the paper. The only difference is that, technically, you don't have to, and you can avoid it if you wish.

Why do we have such a weird situation?

There is a long and complicated history here; what follows is mostly a precis of this paper, which is an interesting read.

This particular journal seems to be using an unusual holdover from an old-fashioned way of handling page charges.

Page charges date back to the 1930s. (You may want to remember this the next time you see someone saying that paying publishers is a shocking modern development.) The majority of journal subscribers at this time were individual members of scholarly societies, rather than libraries, and so there was a fairly low limit to how much you could reasonably charge for a subscription.

However, particularly in physics, the amount of stuff people wanted to publish was growing dramatically - Physical Review doubled in size during the 1920s, and even then still had a growing backlog. Printing and mailing larger issues more often obviously costs more, but subscribers would balk at rapid subscription increases, and the societies were already (mostly) losing money publishing the journals to begin with. The solution by the American Physical Society (followed by many others) was to shift part of the cost onto the authors, allowing the cost charged to subscribers to stay the same even if they now got more pages in their journals, or if the amount of papers dramatically fluctuated in a given year.

But not everyone had the money to pay the charges. For the first couple of years, a generous benefactor paid for everyone who couldn't; after that, unpaid charges mounted up. Some institutions and funders were asked for donations to help cover the gaps, but, critically, authors were not penalised for failure to pay, nor were they chased for the money. The sense that these were "optional" charges became quite well entrenched, and while most authors paid, many avoided doing so without complaints. The US government gave tacit support to the emerging model in the fifties, when it was decided that federal agencies could pay page charges as long as they were the same assessed on non-federal authors, and they were voluntary. (You have to love the logic of "we'll pay if voluntary, but not if mandatory")

By the 1970s, page charges were well established in the scholarly landscape, and almost 40% of US-published articles were in page-charge journals - higher than 80% in some fields. (It was much lower outside the US.)

In the 1970s, the US Postal Service got involved. They took the position that a page charge was essentially a fee to distribute advertising about your research, which would mean that the journals got hit by much higher postage charges than if they were simply distributing public-good information. The IRS made a similar argument about payments being commercial and threatened to increase taxation. The negotiated solution was to very clearly emphasise that page charges were a voluntary contribution, rather than a mandatory one, neatly evading some of the legal issues.

Page charges mostly died out after this. American society journals were always the major users of page charges, but during the 1980s, most of them were absorbed by commercial publishers (who almost without exception stopped levying page charges). Many of the remainder, presumably, found that they could shift away from page charges by taking advantage of the very dramatic increases in subscription charges during the 1980s and 1990s (the famous "serials crisis").

But you'll still find a few today - eg PNAS, or the AGU titles. Most of these now structure page charges as mandatory - I suppose the complex financial issues from the 1970s have now been solved in other ways, or else the fact that you can ask for a fee waiver means they still technically qualify as "voluntary". Not quite sure how this circle got squared... but, regardless, that's where we originally got the "voluntary" text.