It is
far safer than not having a rod.
Realistically, any electricity that has already jumped a km or more of air is not going to care if your house has a metal rod or not. If it is the closest object at that point it will be hit.
What happens next is why the rod is safer. Without the rod the electricity will find a path to ground. Remember, it has already jumped km of air so it has the voltage behind it to go down through cement or enter rooms and find a path via what ever or who ever is closest to the entry point. That can cause masonry to explode and wood to burst in to flames due to the enormous power present for tens of microseconds, damaging buildings and likely killing anyone too close to it.
Now with a rod it has a preferred conductive route and the result is far less voltage to bother the building. It is not totally without issues to consider, as if the rod is too thin it too can explode in to metal vapour or just melt and become useless, possibly even a fire hazard, but if to any reasonable specification it will take the brunt of the energy away from the building.
Now it won't guarantee safety, as you are aware you can get side discharges due to the high voltage along the conductor (mostly due to inductance and the rate-of-change of current) but it is far less than no rod, and you can take further steps to make it safer. For example by having several conductors to earth around the building and having them cross-bonded so it is a bit like a metal cage. That keeps down the voltages seen inside and by sharing the current also increases the capacity to cope with BIG strikes. In addition the electrical system should be bonded to it so you don't get a big
difference between the two. Your absolute potential is not important, what matters is the potentials you can simultaneously come in contact with.
Finally you often get damage to electrical equipment due to the induced surges on the power (and data) cable. There are Surge Protection Devices (SPD) available and if you have lightning protection then they should be 'Type 1' with high energy handling (as it is assumed you have the LPS for a good reason).
If you want to read about it, this catalogue (17MB PFD document) has a lot of information about good lightning protection design:
