I have heard that leading cryptocurrency exchanges are engaged in such activities.
That's right. It has become a trend amongst exchanges to offer OTC services because of the demand. Fee wise it's much more interesting because you can skip the part where you lose 10-15% in slippage by paying a broker a ~3% fee and get spot value without affecting the actual market price. Pretty neat.
In any case, if you plan to make OTC transactions with huge amounts, then you should listen to the advice on the forum in the last place. Perhaps the experience of your friends or acquaintances of your friends can be valuable in this case.
I would just recommend people to consult the exchanges offering OTC services because they will be dealing directly with one of them. It's always better to get information straight from the source than to have people on social media or friends say something that might not be of any help to you.