Street trees — how commonly is a new tree planted to replace the one that’s cut down?

Here in Germany it's quite common. I still weep inside though, because a freshly planted tree doesn't really replace a 50 or more year old tree and with the ever decreasing ground water I suspect it will have a hard time getting its roots deep enough fast enough to survive.

This largely depends on the local government and politics. In my experience in California, many local governments are strapped for resources, so they often won't replant unless citizens demand it or even offer to care for the trees once planted.

In other areas, there is no municipal forestry department and planting is completely up to private property owners who often decline to plant trees. As I've mentioned in other posts, the benefits of trees can be nebulous and widespread, making them less apparent to homeowners, while maintenance costs can be quite obvious. This incentive structure does not always favor planting trees. The biggest motivators are often aesthetics, shade, or home value, so these can be things to stress to persuade property owners to plant more.

Ideally, I think all urban areas should have an operating budget sufficient to plant and maintain sufficient trees to reach about 50% canopy cover. This is a lofty goal but I think it would be achievable with the proper infrastructure and effort.

Almost always in Portugal. Like someone else commented, it does hurt a bit to cut a maybe 50 old tree for one that is 10-15cm in diameter but in some cases I understand, some others I don't and feels like a crime but yeah most are replanted. Most cities and towns don't really want barren streets due to extreme heat in the summer. If anything they plant more trees to fight it.