Just remember, whilst named "Regulations", BS 7671 is not law and is merely a British Standard; it has no legal standing what so ever.
It does have a moderate endorsement from HSE in the front, but that is a little "wishy-washy".
That said, it is the best that we have. It is referenced in building regulations for compliance; scheme providers also mandate this compliance for their members as a minimum level of workmanship.
The requirement in the clause is NOT that all cables are supported using non-combustible fixings, nor is it, as suggested in your thread title, only required over doorways,
I have, I think, answered this question in this forum elsewhere recently.
The clause states:
"521.10.202 Wiring systems shall be supported such that they will not be liable to premature collapse in the event of a fire.
NOTE 1: Wiring systems hanging across access or egress routes may hinder evacuation and firefighting activities.
NOTE 2: Cables installed in or on steel cable containment systems are deemed to meet the requirements of this regulation.
NOTE 3: This regulation precludes, for example, the use of non-metallic cable clips or cable ties as the sole means of support where cables are clipped direct to exposed surfaces or suspended under cable tray, and the use of non-metallic cable trunking as the sole means of support of the cables therein.
NOTE 4: Suitably spaced steel or copper clips, saddles or ties are examples that will meet the requirements of this regulation."
It is also quite restrictive to read individual clauses of the standard in isolation—for example, the requirements in Part 1.
However, on to your next questions.
The requirement to prevent premature collapse extends to ALL premises and ALL cables.
Low and extra-low voltage, so 3ph, single ph, CCTV, network, TV aerial, security alarm, phone etc.
Note that the emergency lighting and fire alarm standards are over and above the requirements of BS 7671, so the first level of compliance is to 7671, then 5266/5839 on top of this, not instead of. These standards have other requirements over and above those of 7671.
There is a big misconception in certain trade groups that BS 7671 ONLY applies to mains voltage wiring; this is completely wrong.
If correctly selected and erected, there is no issue with running wiring above external fire exit doors.