All of my teachers back in the late 70s and early 80s in Ireland had achieved top academic honours in their teaching subject. I know this because a cousin of mine applied for a job there and was turned down because he only had a 2:2. He got a job teaching and coaching rowing in England...
The expectation of excellent degrees worked out really well for science subjects, English, Irish, French, German, business related courses, art, music, etc. Some of them are still teaching, and are owners/teachers in successful grind schools in Dublin.
In the case of my maths teachers academic results did not translate into ability to teach maths to students who weren't capable of understanding maths at a speedy pace. In fact, I think it put the teachers at a disadvantage and thus many students were left fending for themselves or going to grind schools. High flyers don't just achieve, regardless. Many students will find ploughing through calculus difficult on their own. In the Irish system, students must do core subjects plus optionals, but those heading to university must have sciences, mfl, and humanities subjects in addition to maths, English and Irish. So it behoves teachers to be able to actually teach if maths is their subject. Students must take it, and pass it.
To be fair, there were maths teachers in my school who had excellent degrees and were able to teach too.
Also, to be fair, I have no direct experience of teachers who did not achieve great academic results.
The teachers I had all had excellent written and spoken English too. There were two published authors/poets among them, one went on to head a national arts organisation in Ireland, and one had been a leader in the Irish feminist movement and went on after teaching to lead a government commission. I agree with Echt that this makes a huge difference.