My personal experience lies in precision mechanical assemblies rather than optical ones, but what I’ve learned might be extendable to the general topic:
When I make a request to a manufacturer (typically a machinist), I view my submitted bundle of drawings as my proposed contract with them. Or so I was taught. Every single length, angle, radius, number of zeroes after a decimal point, is a line item that I expect the machinist to bill, fulfill, and measure, with documentation, before delivery. You can see the tradeoff with calling out more things or fewer of them. I want to call out enough specifications so my design works as intended, but not so many that total price is egregious.
If the manufacturer met all my line items but the assembly didn’t work, it was on me. But if they had accepted the job and came back short on something I had specified, it’s their professional obligation to rework my assembly (or totally remake it!) to the fine print. You would know whether they came short by having your own internal metrology department make sure they met your specifications. In any case, their prior knowledge that you’re checking the parts they deliver is a great thing.
If I had a highly specific function my design was trying to fulfill and no typical metrology tool would satisfy what I wanted to specify, that’s totally cool too. It’s not out of the question to make an entirely custom testing tool that I give to the machinist to use (to qualify the part for acceptance), as long as I called it out on my drawing for use (they would need to accept the proposed method). For example, for what’s called a go/no-go test, I’d manufacture a set of peculiar elliptical rods to binarily check a peculiar elliptical hole in a workpiece for fit, rather than use a CMM to painfully probe and fit the entire surface profile against CAD. Overall, testing on both sides is ideally transparent, always discussed and not assumed, such that there was as few ambiguities between parties as possible.
Overall, many manufacturers are super nice people and they want you to be happy with your parts. Your continued business is worth a lot to them, as well as your recommendation of them to your colleagues. Such has been my experience, at least in a field where physical form and fit matter more than imaging and illumination properties.
More on topic, but for a single element and not an assembly, Kate Medicus recently gave a recorded colloquium talk about how it takes around 32 parameters to specify a single biconvex singlet for manufacturing. The audio quality isn’t great, but Kate’s talk is assisted by very clear slides. I found it super interesting and think other readers might too.