The “double taxation” issue is a valid concern but with higher tiers inevitably retracting to mandatory service provision, it is likely to become ever more common.
It is already a well established principle of higher tiers off loading toilets, car parks etc to town and parishes many of which naively, greedily empire build without the skills, forethought or capacity to actually manage these new liabilities.
As to fixing pavements and cutting back trees - there are 2 distinct issues here but both relate to ownership. Example a PC arranging the cutting of a tree that it doesn’t own is criminal damage - just as if one neighbour cuts another’s tree.
Highways are even more complex and I can’t remember off the top
Of my head but there are specific statutory obligations (and restrictions) upon work to and on the highway.
Are you asking the question from the perspective of a council that wants to be proactive where a higher tier won’t or are you asking if your councils proposals / actions are appropriate?