Rental only makes sense if there is a marketplace for used machines. Eg, planes and plane engines are components that aren't really tied to one place or company. (The "that aren't easily replaceable" from the parent post.)
But industrial robots for car manufacturing seems like rather specific hardware. If, say, the Ford plant in Claycomo, Missouri no longer needs a machine for making the F-150, who is going to rent it? How is rental a better cost-savings for Ford than buying the machine and later selling it?
I tried looking this up, but failed. The closest I found was that "over half of industrial robot purchases in North America have been made by automakers" at https://www.robotics.org/blog-article.cfm/The-History-of-Rob... .
Also, '"rent" the maintenance contracts' doesn't make sense to me. I sell maintenance contracts to my customers, I don't rent them, and I don't understand what "rent" could even mean in that context.
The parent comment mentions that Delta rents their airplane engines. I imagine that they have the capability to do general maintenance on the engines, but that the engines need to be periodically sent back to the supplier (probably GE or Rolls-Royce) for a teardown, safety inspection, and rebuild. Without regular inspections an engine can't be flown, and is essentially worthless. Not much point in actually owning the engine if you can't use it.
With that in mind, I can see support contracts as an operational expenditure.
But if "over half of industrial robot purchases in North America have been made by automakers" then that's a lot of capital expenditure. I never got the feel that the companies which make modern industrial robots primarily rented them out (akin to IBM's renting out of tabulation machines 100 years ago). I really thought they mostly sold the robots.
An assembly line isn't really a "product," per se. It's more of amalgamation of several products and technologies, many legacy, that forms a cohesive but loosely-coupled whole. You may have several vendors' products / systems in a line. So what you end up with are ongoing contracts that provide for installation, programming, troubleshooting, maintenance, etc.
There's actually a whole specialized industry that does nothing but design assembly lines. It's pretty neat.
There's Boeing which also used to have an airline. It was made illegal IIRC.
And there are things in between these two extremes.
Some airlines have a heavy maintenance organization. Some have outsourced it. Different companies have different market segments and safety records etc.
The point is, there's no one true way for all.
In other examples, many airlines do lease airplanes, and even among the airlines that do own the planes, they still usually lease the engines.
As the GP said, there's a balance to be struck. Delta doesn't have the expertise or the economies of scale necessary to build their own engines from scratch, but they do have the ability to lease those engines and then have their own teams maintain them. Similarly, most companies don't have the know-how or the EoS to run their own data center, so instead they buy cloud services and then have a smaller team to maintain it. It's a win-win. Some companies like BofA might be big enough where they can run their own cloud and it be cheaper than using a cloud provider, but that's definitely not a common thing.