IMHO straps or trays are a MUST.

I've run into situations... (e.g. multiple bee stings while flying! ) where not having had a tray or strap would have resulted in the loss of a plane.

I also dropped the TX due to sweat and high heat, and thanks to a tray/strap there were no real problems recovering.

I prefer a tray over a strap, because a well designed tray will prevent you from accidentally moving the sticks if the TX slips out of your hands.

I've had a TX slip on a strap, which caused the engine to run up fully.... with the tray this could not have happened the way it did.

When training people I find the strap or tray quite useful, as it lets me keep one hand on the trainer switch while I adjust their buddy box, or help them move their sticks.
The tray keeps the TX in place.

A good lightweight tray adds no "neck pain" or noticible weight.