It's completely reasonable to believe that a given person should be capable of quiet enjoyment of their property without having to purchase everything remotely close to it.
Really?
If a ship sinks at sea, and there's a deserted island nearby, does the first passenger on the ship that arrives on the island get to claim it and prevent anybody else from stepping onto the island? Do all those other people on the ship get a vote on who can step onto the island even if they were not there first?
Does owning a piece of property give you the right to veto a particular person purchasing the neighboring property because you don't want then next door?
We as a society have set up a bunch of rules as for how much control people get when they "purchase" property. It's not a single thing, it's actually a bundle of rights, and we have chosen a particular bundle, and that bundle can be changed, and has changed, over time. Zoning is a century old invention.
The idea that a single land owner in an area can block the sale of land to others is considered ridiculous by most. But how much more ridiculous is it then saying that somebody else can't build apartments on their land, particularly in areas where lack of housing has caused massive homelessness and and skyrocketing of housing prices.
Your suggestion is much worse. It'd require millions of dollars.
Doing this might also get yelled at by another activist group for buying up all the lands in the city.
A better alternative: we could just join city council and vote to reject any new building.
Not that I agree or disagree with NIMBY, it's just that your suggestion is much worse than the alternative for NIMBY-ists.