Just to add our wills (UK) are written this same way - inheritance to our children but if they’re dead to our siblings and if any of them are dead then to their children. I’d be horrified if any of our siblings tried to cheat the children out of what we wanted.
Does your will specify what would happen to the share due to any of your children if they've had their own children but then subsequently die before you do?
By the way you've written it here, it sounds a little ambiguous. i.e. if you had three children and each of them had two children, but one of your children predeceased you, it could be argued that your surviving children each get a third and the other third is split between your siblings; whereas surely you would want their children (your grandchildren from them) to have their deceased parent's third, wouldn't you?
Also, is it clear that you siblings would only get anything if ALL of your children had died (and you had no surviving grandchildren)?
It can be a real minefield. There was a thread a little while ago where a grandparent (whose wife had already died) had left money 'for the education of my grandchildren X & Y'. His daughter, the mother of X & Y had then spent the money on private school for her kids but then, some years later, her sister had children (having always maintained that she never would) and expected a share of the (already spent/committed) money for private education for her kids.
Legally, the grandfather had left money for his two named grandchildren, so their rightful money couldn't be partially spent on their cousins, but it would be reasonable to think that, had he known, he might well have wanted ALL of his GC to benefit equally, even those he never lived to meet.
Personally, I think that (assuming you've had children, of course), as you can never guarantee that all of your GC will have been born before your death - especially if you have one or more sons - the fairest way is to leave everything equally split between your children with the proviso that their share stays in their own family/line of descendants, should they (or even their own children) have died before you die.
Of course, there's then the possible scenario where your adult child predeceases you having been maybe very happily married and truly mutually devoted to their spouse for 30 years but without ever having had children. Do you then split your bequest between your surviving children or do you consider that your DIL/SIL with whom your DS/DD shared all of their money (as well as their life) for decades should therefore be entitled to the share that their DH/DW would have had, had they lived longer? Personally, I would say that they should, but it's a controversial one. And what if they'd been together but never married - or been together for 1 year, 2 years, 5 years?