If I recall correctly, I'm pretty sure Toad had this as an editor option back when Toadman was the author, but it seemed to have been dropped at some point over the years. Pretty much every other IDE I use has this as an editor option, and when enabled, applies it when you save the file.
I must admit, I hate trailing whitespace, especially in Git repositories, it's just character noise / bloat. I have a Replace Macro using regex setup for doing it:
Find : [ \t]+$
Replace With :
but as there is no option to assign a keyboard shortcut to a macro (something I asked for here,) it makes it quite cumbersome to use.