Curve tool / Bezier curves tool
Description
A tool which allows you to create a line with multiple nodes. There should be an option to add nodes at any place in the line. When a point is moved, the line should adjust to create a curve. After that there should be a way to add that curve into OSM as a line. This tool should also be usable on existing ways.
A possible alternative would be to use Bézier curves but it might be more complex for most people.
Possibly related issue: #2570 (seems like it's about creating parallel lines rather then creating new curves)
Screenshots

Will this tool be something you select or switch on when you need it or a constant that will automatically create curves?
There are too many instances where a curve is not desirable and therefore I would favour something as an extra that can be switched on or selected when needed.
It should be a tool that you can turn on and off like it's done in JOSM with the buildings tool.
Wouldn’t this give a user the impression that our data model supports Bézier curves (which it does not)?
BTW: somebody actually proposed Bézier curves for API 0.7: https://wiki.openstreetmap.org/wiki/API_v0.7#B%C3%A9zier_curves
It may give such impression but I don't see a problem with that.