Three flaws in your treatise Edward C.
The first clarification is that nuisance does not have to involve damage. The Network Rail case made this ever so clear, and is bang up to date. So, there can be nuisance from encroachment without damage, and it can be actionable of it's serious enough.
The second is that a tree owner can abate a nuisance by cutting branches or roots on the neighbour's land, with the consent of that neighbour, as part of an agreement to abate a nuisance or an offer to do so. The exception for TPO trees makes no distinction as to who abates or prevents, it is the nuisance that is important.
The third is that an encroaching branch that is causing an actionable nuisance can be removed to abate a nuisance, not to prevent it, and the 'abate' exception is therefore available to the tree owner, not just the 'prevent'. That's what the Act says.
There are even circumstances when abatement would requires removal of the whole tree. Unusual, but legally competent.
It's not dangerous ground at all. The TPO exception is clear and can apply to non-damage nuisance to a neighbour, and abatement or prevention of it by a tree owner. The risks are these (i) using the exception for trivial nuisance (ii) ignoring possible alternative solutions to pruning and (iii) doing more than is necessary.
I'll reword it as a set of simple rules.
If a TPO'd tree is causing or willl foreseeably cause nuisance to a neighbour, the tree owner may prune roots or branches or roots on his own land (or, with the agreement of the neighbour, on the neighbour's land) without the Planning Authority's prior consent, as long as (i) the nuisance is or will foreseeably become actionable (ii) possible alternative solutions to pruning have been considered and ruled out and (iii) no more is done than is necessary to abate or prevent the nuisance.
Hopefuly that's clear now. If not, a re-reading of Network Rail and Perrin will do the trick. The ground is only dangerous to tread on if uninformed or reckless.
I leave you with another pespective. If the exception could be used but the tree owner instead asks the LPA for consent, the LPA has no duty to consider the issues of nuisance and can not be relied upon (or called upon) to resolve a civil law dispute. Statute provides exceptions and expects that they be used. What would the justification be for th TPO application works? The prevention or abatement of a nuisance? If it was and I was the LPA, I'd bounce it and invite the applicant to use the exception. It's what it's there for, and what the LPA's not there for i.e. arbitrating in legal disputes.