Should the minimum reasonable requirement be that the
teacher is a native-born speaker?

Of course it should. However, there are exceptions to every rule. If a person is born in Russia for example, and his/her parents emigrate to the USA when the child is 1-year-old, that child will be raised in the USA, essentially having English as their first language.

I have met many native-born FT's who can't spell and who think 'Grammar' is married to Grandpa!
Minimum 'requirement', (in parentheses because I'm using the term lightly), is a 120-hour TESOL course. Personally, I don't think that 120 hours is long enough, but it's not up to me to make the rules.

Pottery degrees or degrees in ballroom dancing etc, only go to prove that the holder has enough English ability to be able to study in a NES university, and has nothing at all to do with their ability to teach English.

There are also huge differences between Turnoi's 'dancing monkeys', that work in crappy training centres, and FT's who work in schools.
We have a new colleague this semester who has been working in a crappy training centre for about 4 years, and he is struggling big-time in our middle/high school environment.

The biggest difference appears to be that although training centres are 'crappy', for the most part at least, students actually want to learn. In schools, they don't. This apparent difference in attitude is something that my new colleague is really struggling to cope with.

In short, he wants to be more than just a 'babysitter', but after 2 years working in the same school, I'm doing my best to convince him that 'babysitting' is essentially what our school's FT's are all paid to do.

Yesterday for example, I had one particular student who was absent from my class, but appeared in our office directly after class was over.
I called him over and asked him why he wasn't in class. He scuttled off to the other end of the office and muttered something to his Chinese teacher who then followed him back to my desk. She began to speak for him, but I told her that I wanted the student to tell me. He couldn't. It turned out that he had been to the hospital. In the summer of 2017 this student will go to Canada to study, yet he couldn't even tell me in English that he'd been to the hospital. He is among approximately 30% of students in our department who all have the same level of English ability.......zero! How on earth are we to be expected to teach 17-year-old morons (in English), when they have the same ability as a 5-year-old? They don't care, their parents don't care, yet we are expected to care.

'Babysitting' in training centres is not normally required, yet it's these same training centres that often end up employing the most useless FT's. Something is most definitely 'broken', but no-one seems to know how to fix it.

Perhaps the new classification of the FT working visa may go some way towards fixing the problem, only time will tell.