Eventually the land ends up in the hands of the few willing and able to abuse the land to that level, prioritizing profit above all else.
Assuming that higher density is always better ignores the externalities required to maintain such a system. Higher density cities require more outside inputs brought in from outside the city. Those inputs strip resources from other lands, require input to process the raw materials, and require fuel and vehicles to transport the goods into the city frequently. The city's waste must be transported and processed somewhere, again adding impacts to the environment even if those impacts aren't directly felt within city limits.
If the goal is to minimize impact, cities would only be as large and as dense as they can reasonably be self sufficient. That doesn't preclude trade between cities, states, and countries, but it does mean the city isn't entirely dependent on a constant churn of bringing in resources from elsewhere and shipping out waste.
Now for the first paragraph: This is kind of the point because maximizing use generally means more density, which means more opportunity to minimize use elsewhere. I did outline one situation that I thought was unfair and should be addressed, which is the situation where you buy land zoned one way with a much lower value only to have it zoned another way on you that makes it a lot more valuable. Other than that specific situation, I don't agree with you that your first paragraph is a problem, it's a positive feature.
As far as shipping goes, it can definitely be comparably affordable to ship in products. Though you still have to factor in costs of everything from making and maintaining those vehicles, the oil and gas that moves them, and the costs on the area that actually produced the products.
My point isn't that everything should be magically fixed with more rural living or a perfect balance of density in cities. I'm simply trying to raise the other side to point out that things aren't simple or clean enough to actually run the math on whether dense cities are better or worse at reducing impact on the environment. There are simply too many factors and hidden costs along the way to calculate accurately.
Surely, it can't possibly be that simple. Sometimes that's true, sometimes it is not. If I want fiber to my house in the country I might be paying $30k to get that line all the way to my one house whether I want 100MB/sec or 10GB/sec. In the city it might be shared with hundreds and only need to run a few yards. Same for sewage. Same for police and fire.
Your examples only really touch on one relevant example though, sewage. Sewage isn't really an issue in rural areas, off grid seltic systems process waste on site and more compelling systems can even compost human waste with very little effort. Modern central sewage system only exist because of dense cities, they weren't needed before that.
High speed internet is purely a convenience and really shouldn't be a concern if there's any meaningful environmental impact from it. Police and fire similarly are conveniences that may turn into necessities in highs density areas. I live in a rural area where police may show up tomorrow if I call them now and our fire is mostly volunteer.
I've never heard of anyone having real issues from either. Volunteer fire still respond quickly enough and it's amazing how much less import policing is when people are more spread out and the expectation of turning to police for every problem isn't the norm.
However if all you ever do is drive to the big city I can see how that would take more time and distance.
These resources can be transported to high density living, or spread out across 100x - 1000x area. Which do you think is more efficient?
Building roads, water, electricity costs millions/mile. All this must be built before you even think about shipping resources to support. Then services (schools, hospitals, dentist) -- all of these and services only make sense at scale.