"The lottery isn't necessarily a tax on people that can't do maths; it is possibly a tax on hope, however."
I'll go along with that, but it's a false hope brought on by the inability to do math(s).
"Some people play because it's fun, because it doesn't cost much, and because the chance to win is non zero."
I could roll dollars (euros, pounds, whatever) down the gutter of a San Francisco hill, hoping to find that my coin lands where a bunch of other people's coins landed, and thus collecting the lot. Same outcome ... except I get the fun of watching the coin bounce down the street before some bum adds it to his booze fund. Your way, some bum adds it to his booze fund without the fun. Either way, the chance of a win is non-zero, but the realistic expectation of winning is zero.
"Winning the lottery jackpot is less likely than being simultaneously hit by an asteroid and lightning, but at least if you buy a ticket your chance is above zero rather than absolutely zero (plus there are smaller prizes with merely lightning strike levels of probability)."
See above. I'd rather invest in something likely to profit. I'll bet you'd make more profit over the space of a year purchasing 5 gallons of gas (petrol) and pushing a lawnmower around on weekends, knocking on doors and asking to mow lawns for a few quid. In fact, I know people who have put themselves thru' university my way ... and people who have been forced to drop out your way. My way provides exercise, fresh air & sunshine, too. Which is probably why more people prefer your way.
"Winning other types of gambling (everything you mention, except dice) at least allows for a certain amount of skill and can sometimes be exploited by mathematicians."
Uh-huh. Sure it can. Show me a rich gambler who isn't either effectively "the house", or has corporate sponsorship, which is pretty much the same thing. (As a side note, I can roll straight sevens all day long with an honest pair of dice, by hand, on a sidewalk or on felt. Give me a cup, and I'm about 75/25. Make me bank it, and I'm about 50/50 ...)
"Of course, most people will not have the requisite amount of skill"
Actually, none do. There are gamblers, and then there is "the house". In the afore mentioned back-alley craps game, I'm "the house", the rest are gambling.
"and the few really talented players will find their ability to place bets curtailed (unless, by playing, they are bringing in money from other people..)"
And that, my friend, is exactly how Lost Wages & Atlantic City, me in an alley, et alii, make a profit from people who can't do math. We are the house. You are the mark. Learn math(s).
 No actual suckers have been taken during the typing of this post.