You don't live sufficiently close to the power line pylons.
For lightning protection, the lightning rod needs to be pretty much above you; if you use a vertical rod, the apex angle of the cone of protection can be, for example, between 20° and 75° for a high standard of protection (from cone side to the opposite side), where the 20° value is supposed to apply for a 20 meters high rod and 75° for a 2 meters high rod (as measured vertically from the protected point). This means, in effect, that the rod needs to be directly above the building and most buildings will need multiple such rods, or an obscenely high rod, if they want to meet this class of lightning protection.
In my country, nobody will let you build a house within 20 metres of a distance power line. A really high pylon might be 50 metres high. If you are willing to believe my googled up ballpark numbers above, the power line provides lightning protection of this class barely to itself and to the "reserved" ground underneath.
You could settle for a less ambitious class of protection, but then you need to expect occasional (reduced) lightning strikes at your home, and you'd still need to build really close to the power line and ideally only underground.