To be fair the children haven't paid full fare so I can see an argument that adults, particularly if they have paid the full fare as a walk on fare, being able to sit
By charging less for kids there is an implication that they would need to be moved for adult passengers
I'm afraid I don't agree. You could say the same regarding lots of things, as children fare/tickets/entry are often cheaper than an adult. For example, cinema tickets are cheaper for children but they still take a seat. Should children be turfed out if an adult wants to watch a fully booked showing? If not, why not?
Train companies do things like friends and family and student railcards to try and encourage people in these groups to travel on the trains by making it more affordable, same for 60+ concessions and disabled travellers. On the basis of the argument that not paying the full fare means you are less entitled to a seat, all the above groups should relinquish their seat in favour of a "full fare" paying passenger. Which doesn't seem fair, to me.
If I have paid for a ticket for myself and my children, and then booked seats in advance, then I have done as the train company have required in order for me to ensure we can all get a seat together. Why is my child's comfort of less importance than an adults? Or mine- having a child on your lap on a long journey is not exactly my idea of comfort? The tickets don't say "children's seat reservation only valid if seat not required by a full adult fare paying passenger", so I see no reason for my DC to stand so an adult can sit down.
If having a seat is really important to you, or entirely necessary to enable you to manage the journey, then buy the ticket and reserve a seat in advance- or take your chances that you might not get a seat.
I know sometimes plans can go awry- such as if the train you booked & reserved a seat on is cancelled and you're put onto another train- but that needs to be addressed via the train company, not by demanding children are moved from their seats to make way for you.