I think that you are making perfect sense

It's just an awkward puzzle

I just think that it is an awful coincidence for two William ROUTLEDGE/ROUTLIDGEs baptised in Hayton by Brampton to have the same death date 24 Oct 1838.
Have you seen the actual image of the parish record for the death or burial of the Willaim aged 12? I ask because the death date transcriptions from Familysearch are listed under the "England Births and Christenings, 1538-1975," database, so I wonder where they are getting the deaths from

The other transcription showing the burial of William ROUTLEDGE,
1838 24 Oct William of Croft House, infant
gives more info than the Familysearch, it is shown as a burial rather than a death and gives the same address as the son of Thomas and Eleanor.
There is only one death registration that fits for a death or burial of a William ROUTLEDGE/ROUTLIDGE on the 24 Oct 1838,
William ROUTLEDGE Dec Q 1838 Brampton 25 19
Personally I would have to get it to see who is the informant, hopefully it would be one of the parents, and then you could be sure which William it was.
Daisy