Super common, don't worry! Sounds like he has learnt to read more through word recognition than phonetically? Some children do. (It's how I was taught! Didn't have a clue about phonics until my teacher training). Knowing each grapheme and its sound is one thing but applying this if your natural preference is to simply recognise the shape of a word is another! This will be long, sorry, but hopefully you can glean something useful.::.
If he was one of my students the first thing I'd try and find out is the root of his worries about writing - which will not necessarily be the same as the actual academic problem he is having, which will have a different fix, if that makes sense?! Perhaps the first thing to address from what you say seems to be his frustration and a resulting lack of confidence. So first and foremost taking the pressure off writing for a nominal period might let things cool and then you can reapproach it. Not sure how practical this would be for your son's teacher but is definitely something you could do at home. I've often recommended parents step back from homework for a week in these situations to prevent it becoming A Big Issue for everyone.
See if he can explain exactly what bothers him. Is it because his work gets messy? Because he can't remember the letter he needs next? Does his hand hurt? (That's a legitimate one!) There are lots of reasons children get fed up with writing and it will take some skill to winkle it out of him I expect - hence why we get a lot of 'it's boring' rather than a straight answer! Is it 'simply' the idea of making mistakes? If he is a confident reader and otherwise able in other subjects is it the fact that he is anticipating 'getting it wrong' that causes him to feel upset and frustrated - this tends to becomes a self fulfilling prophecy unfortunately and kids quickly decide they are 'not good' at something because they find it hard. Some children hate to physically see things written which they know are wrong - this is a big problem in early writing and I see it every year. They know how a word should look but for whatever reason can't quite get it down or misjudge how much space they need to write and get muddled when they realise it's about to fall off the page. In your son's case he might know exactly how the word should 'look' but as he is being taught to break it down this could conflict with his way of doing things. 'Nice' is a hard one, does he recognise it on a page when reading? If so it could be the fact he's then trying to use phonics to spell it which is making him come unstuck. His spelling of people is not entirely dissimilar to how the word looks on the page. If his phonics understanding was clear I'd expect him to spell it peepul (or similar) but instead he seems to have gone for the shape of the word (with the descender of the g meant to be the second p).
What's important to remember and hopefully would help to reassure your DS is that writing is a complex set of skills. First you have to listen to and remember the word you want to write, then break it up, then put it back together in order, remembering the correct letter formation, any tricky phonics rule breakers and then judge the spacing - often all quite quickly as the lesson moves on. Miss any of those steps or forget what the first/second/third one was and you can quickly come unstuck. Often all the necessary skills are there (as with your DS by the sounds of it) but putting them all together takes practise and the confidence to keep trying. I know plenty of adults who struggle with the old try try again so it's a big ask for a six year old.
What could you do at home?
Take a break
Get a whiteboard and pen so mistakes can easily be rubbed off (eventually you might want to move to crossing out, mistakes are good to see, but one step at a time)
Check the basics of pencil grip and control - lefties need to tilt the paper differently.
Build his confidence with the physical side of writing so he gets lots of easy wins - i.e. Spell out the word for him so he has a page of 'correct' writing in his own hand. Then get him to break it down and spell it and you write it (if this becomes a problem then you have more of an answer about where he perhaps needs extra support) Model writing mistakes yourself and see how many he can spot.
Ask his teacher about whether or not he could be sight reading rather than using phonics to decode? If so that's fine, but he'll need extra support to use both this and phonics to help him decode/write unfamiliar words.
I've gone on too long.
Some or none of this may help. Hopefully some! Good luck!