I did a 2 week stint like this for a small company once, and the setup took maybe 10 minutes.
In a bigger organization it's probably more involved, but if you set out to make it a standard way you interview some developers, I think it's perfectly doable.
I agree that improvising it when a developer asks for it, which is what I think you're describing, would be harder.
My first development job worked like that--a one-month trial that got turned permanent something like 2 weeks in, at a tiny company hiring at a slow rate.
I'm glad it got me my first gig, but I'm not sure I recommend it. IME, any position that actually gets applicants gets a flood of hopelessly unqualified candidates. (Think: will fail FizzBuzz, even almost a decade after the blog post that started it.)
My first dev job was like this as well, also in a tiny company hiring at a slow rate (I was the only person hired in my time there, and also the only employee). I think that this sort of thing worked for the company I was employed at because the work wasn't very technically challenging so I was able to get on with things quickly and it became more about cultural fit.
It's interesting that the parent is suggesting this for when you have a lot of experience rather than when you have none.
Given the number of people I've interviewed over the years who have 10 years experience and look very strong on their CV, but still struggle with our basic "coding challenge" (on par with FizzBuzz but more aligned with what our company was doing), even before we get to the real interviewing (with another alarmingly high dropout at this point as well), I can't see hiring for a trial being an effective strategy. We would be sinking way too much cost and effort in to it.
It may also result in poor hiring choices because one person's ticket/feature/whatever may have hidden challenges, and another person's might be easier than initially assumed. There's now more randomness involved in what's an already too random process.
Maybe interviews should be a bit less involved, and companies should be more willing to take advantage of the probation period (and employees too, I've seen a handful pass their probation and regret it).
In a bigger organization it's probably more involved, but if you set out to make it a standard way you interview some developers, I think it's perfectly doable.
I agree that improvising it when a developer asks for it, which is what I think you're describing, would be harder.