Usually that’s how people go about it, manually pulling the vertices to get the desired shape. But I guess a tool that could come in handy would be a curve object. You can set it to bezier and adjust the handles till you get the curvature you want, then convert the curve to a mesh so you have polygons instead of the curve.

Maybe the Spin Tool can do a decent job getting you a nice curve?

Also the simple deform modifier can be given a try:

And a good method is to select two faces and Control + E and bridge edge loops. If you increase the number of cuts it makes a nice curve:
