Fools rush in where angles fear to tread...
We used to have The Bell System, they did a lot of work done figuring out what lightning was. The results were written up. First, a general comment and then here are the three measurements that affect a lot of lightning protection decisions:
The general comment is that current kills and voltage spans the gap. You can walk across a carpet and get a 10,000 volt hit (that would be on a gap of about 3/8 of an inch). The high voltage is what breaks down the air and causes the spark to jump. But the current is so low it doesn't cause a problem. Similarly, in a lightning protection system the voltage causes the arc. High voltages cause the arc from the cloud to the ground, and it takes a lot of voltage to cross 500 to 5000 feet. But the current in that arc is what does the damage and the current is what you have to get to ground.
Measured stuff 1:
The current in a lightning strike can be between 1000 amps and 500,000 amps. The typical strike is about 20,000 amps. There is a distribution between the min and max ranges. Think of a bell (or Gaussian) curve with it's average and standard deviation. Well, there is a similar curve for the probability that you'll get a strike at a certain current.
Measured stuff 2:
The duration and nature of the strike also change. A strike can be a few milliseconds, or it can last for around a second. Think of a cloud as a great big bucket of electrons. A big cloud will take longer for the bucket to empyy than a smaller cloud. If you've listened to a radio station or watched on TV and there was a bolt somewhere, you know that the interference caused by lightning is not uniform. Similarly, sometimes the energy is in distinct pulses that might be 20 millionths of a second apart, sometimes you get distinct groups pulses milliseconds apart. People who have been close to a lightning strike have described everything from a single pop to a rapid series of pops.
Measured stuff 3:
There is a concept of a "cone of protection". If you have a high spot, like a rod up in the air, and then draw a cone from the top to the ground with a 30 degree angle, then 90% of the time lightning will strike the high spot and not anything in the cone of protection. I have seen towers get a mid section strike, but it's not nearly as common as a strike on the top.
Now all these measurements were with equipment, nothing subjective to it. So part of what makes one a "believer" or not (to use the OPs terminology) depends on how lucky you were (or weren't) when lighting hit. Most of us only have a handful of encounters with lighting in our lives, so given all the variability of the current, duration and impact of high objects all around us we all have a different picture of what lightning does.
There is a wide range in protection systems because you get to play a game of how likely a certain sized strike would be, and weight the cost of that strike. If the odds of a 400,000 amp strike are one in 2 million, it's hard to justify a super system. A system that can handle a 20,000 amp strike makes good sense, since that's an average strike. The various building/electrical codes, Bell System recommendations and the IEEE recommendations for protection all have quiet subtle assumptions built in because it is so hard for everyone to deal with all this probability stuff. Also everyone has a different level of risk they are comfortable with. If you've got a 2000 ft TV tower, the probability of being struck is high, and the cost is high, you do a lot. A house is a small foot print and is low to the ground, it doesn't get as high quality of a protection system.
Note also that the currents here are so high that they are outside of our everyday common sense. That's why you see a lot of codes on what sized conductors to use and various ways to terminate the wires. There are approved ground rod clamps, and you can also weld the wire to the ground rods. It's hard to have common sense about uncommon things

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My personal beliefs on all this should be clear from my earlier postings.
One last comment on the wire that goes from the rods or roof to the ground. A lot of the energy of a strike, particularly in the early stages, is at radio frequencies. This is why lightning crackles your radio and can be "seen" on your TV. High frequency signals travel predominantly on the surface of a conductor. So a lot of cell sites and towers use copper strap from 1.5 to 4 inches thick for grounding things. The woven copper wire is mostly for ease of installation, but it also increased the surface area when compared to a solid conductor. As for copper vs. aluminum, as has been already pointed out copper has a higher melting point, so when all that energy is in the top thousandth of a inch of the wire the copper can get hotter without melting. Copper also has a lower resistance than aluminum, so it heats of less. Copper, especially in the ground, is better at resisting corrosion. As for size, the bigger the wire the less the resistance so the better it can absorb the near instantaneous heat (no matter what the material). Note also that even big wire like the stranded copper ground wire used in a lot of systems can build up on the order of 10,000 volts of drop across it during the peak of some strikes.
The one thing you have to be careful about with either metal is the normal precautions for galvanic protection. If you put your copper cable directly on your tin (or zinc-tin allow) roof, there will be corrosion of the roof at the points of contact. So before you go mixing and matching materials, learn about this stuff. I've gone from copper to stainless steel, and from stainless to tin to avoid galvanic corrosion. I also have sacrificial anodes in the ground.
I have all my buried wire in conduit so that strikes to that ground (and trees) have a lower chance of getting into the house via the conduit. Most conduit is good for around 10KV of insulation. Note that even here I have to hedge with the word "most", which reflects back to that probability thing.
Finally, you have to have a good ground system so there is somewhere to dump all that energy. Towers have 200 to 500 ground rods. I've got 1200 feet of wire in the ground for my ground system. It's another reason to work with someone who understands this stuff and not to DIY it. To the OP, you had a system there, so you can just connect up rods on the roof and _probably_ be ok.
Regrettably, all such discussions on public forums are made with the knowledge that we have more lawyers than engineers in the US. There is more I could say and more recommendations and examples I could make, but no.
People who understand this stuff, please realize I'm trying to simply things here.
Pete