*Schools are in loco parentis. You are responsible for looking after the child while they are in your care. So yes, it is your responsibility to get a child to eat if they aren't eating well, because that's basic care. Primary school children are still very young, especially in KS1 and in early KS2.
Unless schools are going to let parents come into school to help their child at lunch, then yes staff should be doing that, it's all part of the job.
I went to a private school and our lunchtime was a set time when we all sat at long tables and ate at the same time. Once everyone was finished and the plates cleared, then we went out to play. Quick eaters learned to chat to others, slow ones learned to speed up a bit before the course was cleared. Each table was supervised by a teacher sitting and eating with us.
I think a similar system of a set eating time as a previous poster also suggested would help a lot. Fast eaters would know they had to sit and chat, and slow ones would know they had a set time in which to eat. Then everyone gets the same playtime.
My son was one of those who would not eat because he just wanted to go and play, ace I had to ask the school to monitor him a bit because he was starving and so angry by hometime as a result. Some days he was literally only eating a packet of crisps. If I only gave him crisps for lunch and no other food that would be seen as neglect, but people on this thread seen to think it's ok if it happens at school. It's baffling.
I despair of this attitude that children's basic human needs are inconveniencing teachers. Education is about much more than numeracy and literacy and if you don't know that then you shouldn't be teaching.*
With all due respect, we're generally not talking about private schools here and I'll hazard a guess that your experience of school lunchtimes are very different to a standard school!
In my infant school we had 180 children and one school hall for ONE hour. Reception ate first then year 1 and then year 2. This was all with a maximum of 6 MDSAs but usually far, far less. We needed sufficient staff for the playground, sufficient staff for the children eating and sufficient staff to clear the hall promptly at the end of the lunch hour, so that PE/interventions could commence after the afternoon register.
We simply couldn't ensure that every child was given adequate support to eat all of their lunch but we did our absolute best! I said earlier on, some parents complained that their children were slow eaters and encouraged to eat a little bit more and then missed some of their playtime and some complained because they had told their children to eat their (often huge) packed lunch and didn't get much time to run around. We can't win!
We didn't have the luxury of fast eaters chatting to the slow eaters, or that the slower ones would just eat faster!!!! What a privileged experience you had!!!
Oh and each table had a teacher sitting with them? Our teachers barely have time to make a coffee and gulp down a Pot Noodle whilst preparing the afternoon session at their desk! Or replying to emails or ringing parents who criticise the smallest bloody ridiculous complaints!
In all fairness, if that's how you think state schools are then you are severely delusional!
(And have never worked in a state school!)