We live in a large city so it isn't unusual to see people take down large old trees. Here you need a permit for any tree removal with a trunk larger than 6" across. Spaces are tight; you don't want some DIY amateur felling a tree that falls on top of the neighbor's roof - especially if you're the neighbor!
There are major problems with the older trees:
Many are not really suited to urban environments. For a while it was the fashion to plant redwoods, because they're fast-growing. If you are familiar with redwoods, this is the absolute worst city tree in the world to plant! For one thing, they get 100'+ tall - and WIDE. If a limb falls off, it weighs over 80 lbs and can kill someone (it happens periodically; crushed cars occur every year during winter storms).
You can't just cut them down, either. Redwoods resprout; unless the interior heartwood is killed, the stump remains alive and saplings will reappear from both stump and roots. I once saw a neighborhood backyd in an open house. where they had cut down a redwood but left the tree on the ground - I guess it was too big and heavy to move easily. The tree had resprouted from the top, and saplings were emerging all along the trunk. Instead of one tree, they had sowed half a dozen new ones, LOL.
Or people planted eucalyptus, which aren't native. They're a fire hazard (high oil content) and their evergreen litter drops year-round, killing all understory plants around them. And sweetgums, whose aggressive roots break up sidewalks and invade plumbing pipes.
It's why most cities have approved lists for street trees. Trees are wonderful, but you need the right tree in the right place, as damagedgoods' post points out.