You're leaving out a few details. First, governments can't "commit" the time of people, unless of course the government is a totalitarian one. (Yes, I suspect totalitarian societies have been fairly efficient at building "Monuments"; cf. the pyramids...)
But the society of Star Trek is inevitably portrayed as completely free. Of course, you will probably retort that the future government of Star Trek has no need to be totalitarian in this sense of "committing" its' subjects' time to building "Monuments". After all, they just tax their citizens at a sufficient rate to build this stuff!
Small problem: they've "abolished money". (!) I heard Picard state this explicitly himself, either in an episode or in one of the films. (Which is weird in a way, because I don't think this was true in Kirk's time, I think they did have money; apparently the Federation of the future "abolishes money" within a span of 70 years or so....)
So if the future society of Star Trek is a free society, and has no money, then how is their government "committing" anything to "Monuments"? What, are people just doing everything that is necessary (sweeping the floors, serving food, etc), voluntarily?
Well, that was the communists' dream, after all.... Nope, sorry, "capitalist" Star Trek ain't.
Actually, there is a conflict on this topic within the "original series", when extended to include the feature films. In several episodes of the old TV series, there are references to the use of money by people aboard ship. While on board a Space Station, the crew members on "shore leave" have to buy drinks. Uhura asks: "how much for the Tribble". People are heard wagering in monetary units which are simply called "credits". The "parallel universe" Kirk tries to bribe Spock.
However, when we fast-forward to Star Trek IV - The Voyage Home, there is at least one scene that leads the audience to think that money is not used in Kirk's time (the restaurant scene). That might be explained away as a cashless (as contrasted with moneyless) period. Kirk's 23rd-Century debit card would probably not work at Pizza Hut.
They did, and they said that they didn't eat real meat. Picard made a big anti-religion speech in one show. Which is why I think Deep Space Nine was so much better. They had crime, vice, and the mob. They had shows dealing with faith, conversion, and other religious issues too.
So if the future society of Star Trek is a free society, and has no money, then how is their government "committing" anything to "Monuments"? What, are people just doing everything that is necessary (sweeping the floors, serving food, etc), voluntarily?
You've given several examples of why Star Trek: The Next Generation was the worst of all the Star Treks. Picard was the liberal ideal of a military officer. And ST:TNG was the liberal paradise. No religion, No money(and by extension no business or private property), and an authoritarian social order with the perfect liberal giving the orders.