There are lots of British children who cannot come to the UK for reasons connected to British immigration rules. There's quite a good article in The Guardian here about one such scenario:
https://www.theguardian.com/society/201 ... hilippinesMy son could not come to the UK when he was first born as his mother needed to get a British visa, which was not initially forthcoming.
Under the current rules, though I am British, I would need a salary of £22,400 to bring my foreign-born child to the UK, a level considerably above the minimum wage. As well as good English abilities by the mother.
I was reading the comments on the BBC Indonesian service and the Indonesian commenters seem to perceive that Shamima Begum is Bangladeshi, not withstanding that she was born in the UK. Her father is apparently living in rural Bangladesh, so you can see the point of view to a significant extent. Ms. Begum's child was born in Syria to a Dutch father, but had British citizenship.
My parents, grandparents, etc. are all UK-born but I happened to be born outside the UK, though I have no ties to the country of my birth or other citizenship than British. When my son was born, however, he wasn't entitled to British citizenship as I had the wrong kind of British citizenship (i.e. Shamima Begum is effectively more British than me in that my child was not British but hers was).
Clearly this comes down to rules - if you don't follow them you can find yourself deported after 40 years, or not being allowed to bring your child to the UK.
In terms of Shamima's baby, he would have had the same option, given his Dutch father, that many thousands of other British babies face - get his British passport and leave the country with his father.
I find it a little unreasonable to make post hoc ergo propter hoc complaints that the baby was not allowed to come to the UK, when nobody is seriously proposing making changes to the immigration rules to allow other British babies similar immigration rights: i.e. in practical terms where a British baby is born to a non-British mother, this would mean the right for the non-British mother to enter the UK without encumberance.