The economic term for this is the laffer curve, which plots revenue gained vs taxation rate. At a tax rate of 0, revenue gained is ovbiously 0, at a tax rate of 100, 0 revenue is gained as well because nothing is being produced. So, obviously, there must exist some global maxima in the laffer curb. What your arguing is that, currently, the NH beer tax is below the laffer maxima and by raising taxes, you could raise revenue. What other people are arguing is that it’s above the laffer maxima and increasing taxes would actually decrease revenue, and thus be self-defeating.
Hey, now! I’ll be the first to admit that the New Hamshire education system has serious problems - but the quality of education really does vary greatly from community to community. In some towns, it’s pretty bad - but I’ll put up the education system of other NH towns against anywhere else in the country. Merrimack, for example, has an absolutely excellent Honors program and a decent selection of AP classes for the high school students. Hell, I basically napped through much of high school (and my grades reflected it), but I was still better-equipped for my freshman year of college than many of my fellow freshmen. A more dedicated and competent group of teachers than the faculty of Merrimack High would be very hard to find.
Further- there are some very good jobs to be had in New Hampshire, particularly if you’re interested in defense-engineering work.
Your point on health care, though, is well-taken.
Local news indicates that the newest pay-for-education plan involves taxing cigarettes. Ah well.