You almost won me over, until the end.
Firstly, the production of ALNM that you saw in the West End was a transfer of the production from the Menier Chocolate Factory so it's another non-profit example. Also, it was announced as a limited season in the West End -- something which is pretty unique to the economics of London theatre (a commercially-viable limited run of a transfer of a musical). Also, that's only one example of the 40 shows you mentioned you saw.
That said, though, the place where you really lose me is in your last paragraph.
While their National Theatre gets twenty million pounds a year, our Public Theatre gets $40,000. This, to me, is a problem. Its a pretty blatant reflection of the way their society values their theatre and the way ours does. They view it as something that is for the people; something the people are entitled to; something the people need and will benefit from. We view it as a luxury--an exclusive club for existing fans, a perk of living in New York and having enough money to afford theatre. Do you honestly think THAT'S why there is a fraction of the government funds allocated for the arts in the US vs in the UK? Or conversely, do you think the love of theatre across the UK is first and foremost a function of ticket prices in the West End?
You acknowledge that there is a severe lack of government funding for the arts but your solution for that is to lower Broadway ticket prices to somehow fix that while simultaneously weakening the viability of the shows themselves???
If anything, your argument supports increased funding in arts education and increases in funding towards regional and local theatres so that people across the country begin to make theatre a more significant part of their lives. It supports non-profit arts centers and producing organizations in New York and across the country trying to create more programs like the National 10GBP program with the help of government, corporate or private sponsorship. All of those things will build future audiences.
But if the primary way that people make theatre a more important part of their lives is by specifically by seeing
Broadway shows, then I guess you need to be lobbying the airlines and hotel industries to lower their prices too, no? After all, the vast majority of people in this country DON'T get to visit New York with any frequency, if at all. If you want to change the culture of the country as a whole as it relates to live theatre (which is what would likely need to happen to ultimately see any change in attitude by the Federal government), there are any number of better places to start than with lowering Broadway ticket prices because such a change would only affect of the tiniest fraction of the people whose attitudes you are seeking to change. Looking, however, to the commercial Broadway theatre industry -- a business first, whether you like it or not -- to lower its ticket prices and weaken its financial viability in so doing, as a means of influencing the national culture is at best naive and at worst, ass backwards.
"No matter how much you want the part, never let 'em see you sweat." -- Old Dry Idea commercial