Right. I thought some more about it and realized that if the option existed for only leaving blocks on in the current scene, then you would have the In, Out, Amp and Cab blocks bypassed in all other scenes by default, which would be a pain. So this probably isn't a realistic feature idea, unless you had the ability to fine-tune the default bypass state for every available block type.
Currently I've been adding a new block, using the keyboard shortcut to bypass it in all scenes, and then enabling it only in the current scene. Seems to work fine for me.