You may have mis-read my post, I stated that "The market maker will manage his book for *everything* that is on his book to retain a largely neutral stance." (By 'everything', I meant within that particular name'.)
This is in exact agreement with your reply about them wanting to hedge themselves.
Your original post stated "buying call options (which then force the broker to actually buy the stocks)".
This part is not correct. The market maker (MM) is on the other side of your trade (not the broker) and the MM is not 'forced' to do anything. (Some may see this as semantics but the broker is not the MM and saying the MM is 'forced' suggests he is obligated).
The example I gave was deliberately simplistic to explain the point, we've ignored premiums, differing strikes, calender spreads etc.
The MM will manage his book as a whole.
I really wanted only to point out that buying a call does not necessarily result in the market maker buying the underlying.
I'm not saying they *never* have positions in the underlying as well, of course they do, but its more complex that your words suggested is all.
Here's a couple of scenarios to consider...
The stock is trading at $300 and I buy a $275 Call for $50 premium.
The stock then collapses the next day to $75 and stays there until expiry. The $275 Call I've bought is now worthless and I've lost my $50 premium.
If the market maker was 'forced' to fully hedge and bought the physical at $300, he's now lost $225 less the $50 he got in premium from me.
That means he's out of pocket by $175. So as you can see, they need a more sophisticated solution or they'd go broke pretty quickly!
As an aside, there is certainly money to be made buying out of the money (OTM) Puts.
How much is a $40 put worth when a stock is $300. Answer - pretty much nothing.
How much is a $40 put worth when that stock falls to $40? Answer - A whole lot more because although the intrinsic value is still zero, there is still 'time value' which increases as the option approaches the strike price.
So if I believe GME is going to $40 by the end of March, I could buy a bunch of March $40 puts for next to nothing while the price is $300. As price falls, the value of the $40 put increases even if it never actually gets to $40.
However, as per your link, in this particular case the crazy volatility led to some 'interesting' options pricing but I've shown the principle that buying a deep OTM put can still produce rewards if traded properly.
Again, these examples are again simplistic so people can follow along. Professional options trading is more complex and its understanding this complexity that leads to interesting strategies that's aren't possible trading just the physical stock.
Since I appear to have gone slightly off-topic so I'll stop here!!!
Hope it helps. Its a fascinating world to enter for those inclined to do so.