I think the default behavior of each tool works well. Most of the time I want to change the SHAPE of the radial tool without changing the center location. Most of the time I only want to crop from ONE side of the crop box, not both sides. The defaults nicely work this way. In my opinion there are a LOT of UI inconsisteinces and downright odd/terrible UI design in Lightroom but this is not one of them.
The worst UI inconsistency is between Lightroom and Lightroom Mobile. The NEW Mobile looks more like Lightroom with its right panel and whether this is good or bad is another issue considering the photo is smaller. The problem is they changed all the names of the tools and headers and moved the tools around when they didn't have too. It would have been just as easy and more consistent to make the panels with the same names and order like Lightroom. Hopefully the new Lightroom Mobile panels aren't what Lightroom 7 is going to be like.