Mine went through phases like that. I definitely would NOT have saved their meal. At home, once they calmed down and had time out (timing time outs only began when they sat quietly on the step, of they move off, it started again, if they screamed, it started again, if they tried to hit me they got another minutes added on, and it started again).
At 4 they're a bit young to go hungry, so would offer something very plain to fill the tummy, AFTER they had calmed down and apologised.
When they fit older they had to state exactly what it was hey were apologising for, they had to state the bad behaviour. At 4 they're old enough to say 'sorry for screaming' or 'sorry for hurting you'. And yes, early on getting them to state the specific behaviour could lead to further tantrums.
This period can feel eternal, and it would sometimes go for months of frequent extreme tantrums before would die down again.
However, once the tantrum and punishment is over, then it needs to be OVER. You can't keep bringing t back up, and you can't stay in a bad mood.
I have had to, on occasion, say 'sorry, mummy is still feeling very upset. Sometimes when you hurt someone they can take a little longer to feel better. You need to play quietly on your own until I feel a little better' it does them no harm to know that their actions have can have longer consequences on others , especially if your child has tantrums in other settings, like nursery, hold indeed or school.