Okay start with a simple model. Tens of thousands of volts (pick a number, say 50,000 V) and hundreds of thousands of amps (pick a number, say 500,000 A). Pick a really big wire for your new aluminum mast, say 6 AWG, and look up the resistance per foot. Look at the cross-sectional area of the mast and estimate the resistance per foot. A little E=IR and a little P=IE. Pick an ambient temperature and look at the temperature rise in the material and compare to the melting point. Include the cross sectional area of all your rigging. Take credit for high humidity atmosphere (the model is getting more complicated) and even rain on the mast and deck. Look up the melting point (and sublimation point) of epoxy resin.
What you are going to find is that the path is indeterminate. We can play with macroscopic Maxwell's equations but we are seriously into non-linear behaviors over milliseconds.
It boils down to being hit by lightening is very very bad.
For empirical data, take a look at post event pictures of wooden masts hit by lightning. Look at masonry chimneys hit by lightning. Trees.
In the absence of any numbers this isn't a particularly convincing argument. But I get it - your opinion is that its pointless to do anything.
Listen, you may be right!
I think its a little less hopeless than you are making it out to be though.
By the way, 0AWG copper (little over a quarter inch diameter I think), a commonly specified lightning down conductor, has a resistance of about 0.0001 ohms per foot of wire. Assume you've wired that up to the top of your mast, so its a, say, 50 foot long down-conductor. Next, google will tell you that the average bolt of lightning carries 30,000 amps of current. V = IR, so the voltage drop across your down conductor when it's carrying that load is 30000 * (50 * 0.0001) = 150 volts!
Thanks to your trusty down conductor, you've pretty dramatically neutralized the problem, at least in the space between the top of your down conductor and the ground.
I don't know how to calculate how long that wire can handle that current before it gets too hot to be useful, but a lightning strike is not a long event (10s of microseconds).
OK so most of us are just using our mast and our rigging as our down-conductors to get to deck level, not a big fat 0AWG copper cable. Luckily the tradeoff in conductivity per cross sectional area is made up for by, well, a lot more cross sectional area! In my case, the total area of my uppers (made of stainless) and the mast section (made of aluminum) *blow away* the current carrying capability of a 0AWG copper cable.
And as a final point, lightning protection systems are almost ubiquitous on tall structures in lightning prone areas, and there are guidelines for sizing lightning down-conductors, and you simply aren't going to convince me that its all malarky. That's all I meant by "I dont want to debate this".
All that and it may still not work, but its certainly not as futile an endeavor as you make it out to be.
After all that, sticking an antenna up on the top of the mast and wiring it straight into your living quarters certainly feels silly. Which, of course, is the point I would /like/ to discuss with anyone else who has considered it.