Stupid Question. Why not run Power up a Tower ?

Silly really.

It seems that we can run cables into Buildings to carry 240VAC mains power.

How come it is a no-no for a tower ?

It’d make all the PoE nonsense go away (mainly).

And … does it cost more to put a battery up there too ?

(i got no towers)

in most countries it is illegal

getting zapped while climbing up the side of a tower has a much greater chance of killing you. ( decelleration trauma comes to mind )