I think the real benefit to the consumer of renting from Redbox instead of buying is that Redbox has economies of scale on exchanging movies between consumers and distributing them geographically. If a consumer buys a movie, watches it, and resells it, that's a lot of hassle, whereas Redbox has managed that redistribution by building automation.
I think what happened is they started selling to Walmart et al for the same price.
This article (admittedly from 2008) says studios hate Redbox. And that Redbox gets its DVDs from regular movie wholesalers (I assume where Walmart gets them too).
https://arstechnica.com/tech-policy/2008/10/universal-studio...
I actually don't know the details of Redbox. The specific example I remember is Blockbuster video, which used to get copies of movies for virtually free, in exchange for sharing a portion of their profits with the studios: https://www.quora.com/How-much-do-movie-rental-stores-e-g-Bl...
I think the studios agreed to this because of market segmentation, for any given movie there are people who have no interest in paying $20 to own it, but will pay a few bucks to rent it once or twice. If the studios didn't support this model they'd be leaving money on the table.
It's all ancient history at this point so my memory is fuzzy, but I think hobbyist stores actually had the better business model by that measure (they'd focus on a limited selection of classics that people would rent again and again). Then Blockbuster came along with these studio deals they were able to negotiate based on their volume, allowing them to offer practically unlimited copies of new releases. In conjunction with a decent selection of classics this enabled them to lure customers away from the hobbyists. A combination of pressure from the studios and the emergence of competitors with lower operating cost (Redbox, Netflix etc.) later crushed Blockbuster. And watching the studios raise their fees until Blockbuster collapsed surely contributed to Netflix's decision to produce a lot of original content. And now we're caught up to the present day.
A classic scenario is renting a movie. Let's use DVDs as an example--even though they're falling out of favor, they're a little simpler to talk about, and the economics of online aren't that much different.
Studios like big numbers and would like to sell movie media/rights/access/whatever (it's complicated) to someone who can drive lots of demand. So the rental outlet will get a steep discount on those things for buying in bulk.
Meanwhile, you're not even sure if you'll want to watch that movie more than once, and the resale value of a used DVD after a couple years is basically zero. So renting the DVD at least the first time, and maybe every time you want to watch it, is a pretty good deal.
Case in point, Redbox's "markup" over whatever they're paying the studios is large, but it's still a pretty good deal for you and me.