Alright, not trying to be argumentative here, but realize in that situation the buyer would simply buy more DITM calls. ATM isn't even in play here nor is gamma as we're already well past the inflection point for gamma while DITM.
Just my guess:
A realised loss in the options can be important or even critical, especially if always keeping 100% fully invested in either stocks or options, for analysis sack.
Why not simply buying stocks or keeping just cash after crash?
After crash, buying the same quantity of extremely expensive options, using any cash left after deducting realised loss, will easily generate a big loss potentially, when later the market price recovers and IV also recovers, i.e. at much lower value. Because the second round of buying more DITM could also possibly become OTM in a later date, losing a lot of IV values.
That after crash might be good timing for selling ATM options! Instead of buying ATM! Just 2 cents again!