A buyer's fee is a tax on the side of the market that's hardest to build. A seller has stock that has to move and a reason to be here; a buyer owes you nothing and leaves at the first excuse. Charge them and you get a thinner market, which is worse for the sellers too.
There's a plainer reason as well. Payment runs directly between the two companies, against the sale contract concluded on the platform — we don't hold the money. We're not insuring the buyer's payment, so we don't charge them as though we were.
The seller's side is different: they're getting access to demand and a price for stock that was sitting still. That's worth one percent, and nothing at all until the deal actually closes.