Based on your experience or what you have seen in the markets, do OMM use variance swaps at all to hedge/control their book's risk or are volatility bets (implied vs realized) their actual source of revenue since bid/ask spreads have been so compressed nowadays?
Totally depends on how one trades. We never did variance swaps. But we never ran huge vega books. You try to hedge closest to what you have got on and KISS still applied, also to professionals! If we would run a larger vega position, it's the why and where that's driving that strategy. So IMO, vol is cheap compared to something else... so not "it's cheap all across the board so let's dive into it"... that's just gambling IMO. We ran vol spread within sectors or across several indices. And skew spreads. Or calendars. There's no need for a variance swap then. But again, we liked to keep it simple. But you are right in saying that a main source is/was vol bets and gamma... gamma is basically implied vs realized.
I always loved those less liquid stuff... proper spreads! But you always need to be more aware of any risks in this case, more than in heavily traded stocks/options. Smaller less liquid stocks tend to not follow strict guidelines. So earnings dates will not be set in stone, dividends can be more random, big trades are often involved in some kind of frontrunning or insider info. The upside is when you've hedged properly you can still make decent money and when the trade initiator returns... and they almost always do... when you have the biggest slice of the initial trade, you're more likely to make a very good trade on the closing of the position as well. Or when the position is rolled-over... great stuff!
I will answer in more detail tomorrow, but in general you don't want to have variance swaps in the book unless (drum roll) you want to be exposed to variance swaps. So no, MMs would just try to run a balanced(ish) book and avoid f*ck ups.