I am not sure how much it helps them.
- If they are paying cash for the house (w/o a mortgage) they are paying themselves. That fee will be part of their income. Though if they owe taxes on the profits when they sell, this added expense will reduce the tax they have to pay.
- If they have a mortgage then they are financing their fee. They will pay interest on that amount borrowed for the life of the mortgage. Plus the fee is part of their income. but it could reduce their taxes when they sell.
Generally when the listing agent finds a buyer they get the whole fee, though some will give a discount. The details should be in the listing contract you signed with the your agent, there should also be a section discussing the situation where they are also representing the buyer.
Since you figured this into the price, there are a few options:
You can drop the price below the list price by the amount of the buyers agents fee. The selling agent only collects the sellers agents fee.
You can keep the price at the list price, the buyers agent collects their fee at settlement, the sellers agent only gets the sellers agent fee.
The price stays the same as the listing price, and the sellers agent collects both fees. The two agents then decide how to split the fee.
The two agents will have to agree on the plan.