Air knows there is only a certain price the average customer will pay for a certain type of property. So let's take an apartment that has a $500 total for 3 nights. Since Air's algorithm is a secret, let's just say for this amount they charge a 9% booking fee.
$500 (9%) = $45 + $15 (3% from host) = Air gets $60 and guest pays $545.
Now let's say according to Air's research they know the average customer is willing to pay $550 for this type of apartment. If they force the host to reduce their rates, then yes they can take a bigger piece of the pie. Let's say you reduce the rate by $20, to $480. And let's use a 13.5% fee (like FK).
$485 (13.5%) = $65.48+ $14.55 (3% from host) = Air gets $80.03 and guest pays $550.48.
That wasn't really the best example as there so many other factors that we don't know about. And the nightly rate really isn't that much different when you divide by three. But I just using those numbers to show how sites can take a bigger chunk.
Another thing is the sites are trying to make customers believe the fees are just part of our rates. HA does this, and FK too. I checked Air the other day and it looked like they changed the appearance of where they explained the booking fee, under the pricing detail. I don't recall the explanation being above the total. But I can see them at some point only including everything in the total, and customer just thinks it's all part of our rates.
Even HA said the traveler is more likely to book if they think it is just part of owner rates verus a fee the site is charging.