With respect, that's an ideological stance because you're not giving any scientific, practical, evidenced reasons to not the vax.
I think it's unethical to not give it unless theres individual reasons pertinent to the child from a Medical or neurodiverse pov.
"Protecting the elderly" means in real terms: (off the top of my head as I bet there's more)
•Additional protections on top of their own vax due to lower social circulation.
•Less likelihood of hospitalisation which eases general nhs pressures for beds, ICU, staffing, appointments, waiting lists.
•less likelihood of serious illness which means less reliance on the probability of needing various drugs (free prescriptions which obviously costs the nhs), worsening of other conditions and the need for carers (either nhs or family.)
They can't say it directly protects the nhs and access to Gp appts and nhs funding if a wide variety of services because that's a butterfly effect. But as a whole, on a bigger picture level, it's does.
Not to mention, as stated earlier, child school absences and staff absences. We know that's detrimental to education. (As an aside, There's a very big issue among teen girls with school refusal at the moment.)
Covid has near doubled all those pressures, so the nhs wants to target what they can in way they know work as much as they can.