You're basically saying that when the markets goes down, your DITM call despite being still DITM won't hedge as well as before (delta decreasing) so you could prefer exercising. It makes sense.
That would make the opposite of sense. You are getting shorter on a down move. That's a bad thing?
a) Don't exercise call, hold short/ or sell underlying against it. You're flat but if market craps = Huge win.
b) exercise call. gave up a free put. You're Flat. Market craps = 0.
"Back to the original topic, if you were selling that specific DITM call in a combo like a box, the small profit you get from the early assignment will probably not compensate the troubles caused by that missing option in your combo."
yep, I'll say it again, and preface it again with 'no one listens.' The formula for whether you exercise an option or not depends on you purchasing in the corresponding OTM option. You ALWAYS buy in that f'n OTM option!!!! (Unless you already have a shit ton of long OTM options in that area)

