Modern urbanism is very opposed to urban sprawl because of those and many other reasons. Transport is just one aspect of it.
I'm not sure that higher pollution is innate in lower densities, or whether that is due to the specific way our suburbs are designed today, and the technologies (such as ICE for transportation) that we use to enable them. It feels like an engineering problem.
And sure, putting everyone into a giant anthill might make it cheaper to contain and dispose of all the generated pollution. But then we should be honest and admit that it's about cost, not about what's best.
Small businesses - I don't think there's any innate value to them, in a sense that we need as many as we need to serve our needs, but there's no "right" for any particular small business to be viable in a world with changing conditions. If suburbs can sustain fewer small businesses, so be it.
Segregation is an orthogonal issue. I think you meant stuff like "white flight", but it is a symptom rather than a cause. If you prevent people from moving away, it will not resolve the tensions that make them desire to move - indeed, it may well exacerbate them.
What you refer to as "modern urbanism" sounds like an ideology that insists that it's the right solution for everyone, and those who disagree should be forced into it for their own good. I think that different people have different preferences in this aspect, as they do in most others, and that any approach should, ideally, try to respect those preferences, rather than ignoring them, or pretending that they are irrelevant.
In a car oriented suburb where you have to drive to literally every location you have to try extra hard to get even a basic level of exercise.
FWIW, the suburb where I live is on the edge of a wilderness area. There are several great walking, cycling and hiking trails within a 2 mile radius. Some of those are fairly steep, too, so even one mile provides a good workout. I find that I engage in these activities far more often than what I lived in a large city, and had to drive for quite a bit before getting anywhere bigger than a tiny block-sized park.
