My guess is, it's either op is trying to avoid extra charges from converting his crypto to fiat or he's avoiding attention. There's certain amount that will enter your bank account and you'll be invited by the authorities to proof the source of the funds, so that could be it.
Who would now pay the transaction fee? The transactions will be part of what the buyer would pay as agency fees. These agencies are in business to make money, they don't give free services. The idea of trying to avoid suspicion by the government is a good point. Some countries also have unfriendly crypto laws which might make crypto users want to use middlemen.
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On a personal level, buying properties on the Internet using crypto is something I wouldn't dare because of the high rate of online scams and the large amount of money involved. If I get scammed I'm not sure I'll be able to get over it.
There are some genuine real estate companies that accept cryptos for payments. Bitcoin is a currency and can be accepted by many reputable organizations. 
