I think it would be lovely if you could single left click on a token to “select” it, and have that come with its own options. For instance, there’s a nice tactile feel with clicking on a token, then using the arrow keys to move it one square at a time. This movement would also be nice in demonstrating things to those with the Player View, so you can say “okay, is this the path you’re thinking?” as they watch you move it in real time instead of just dropping it in specific places.
This could be used to incorporate other things that are being considered, such as more specific token modification (double click adds labels, with single click you could perhaps a single letter/number symbol on the token itself to differentiate it). Or, if it is in the consideration, perhaps it could bring up a toolbar that lets you add a simple symbol to it, such as those from game-icons.net.