Perhaps an example helps.
Suppose @RPietila is now in the US (to simplify the example) and wants to buy a bottle of fine French wine that costs 500$ if paid in cash at the store -- just the current market price of 1 BTC -- with free delivery to @RPietila's location. The wine merchant "accepts bitcoin" through Bitpay.
GOING THROUGH BITCOIN:
Years ago, when the price was 3$/BTC, all fees included, @Rpietila bought (say) 1.03 BTC for 3.09$
Today, @Rpietila clicks the bitcoin payment option and is directed to a Bitpay form that specifies the amount of bitcoin he must send, which is 1 BTC plus (say) 0.03 BTC to cover all the costs and fees.
@Rpietila transfers 1.03 BTC to the Bitpay address, shown on the form. Let's suppose there is no fee for that.
Bitpay sends 500$ to the wine merchant's bank account. Pays a bank transfer fee for that, let's say 5$.
Bitpay sends the 1.03 BTC to Bitstamp and puts it up for sale. Let's suppose there is no fee for that.
@JayJuanGee deposits 520$ into his Bitstamp account. Pays a bank transfer fee for that, let's say 5$.
@JayJuanGee buys the 1.03 BTC for 515$ (suppose that, by miracle, the price hasn't changed). Pays a trading fee on that, let's say another 5$.
@JayJuanGee withdraws the 1.03 BTC. Let's suppose there is no fee for that.
@Bitpay now has 515$ in its Bitstamp account. Withdraws 510$ to its bank account and pays a withdrawal/bank transfer fee of $5.
NET RESULT:
Bitpay paid 505$ (including one bank fee) and received 510$ (after all Bitstamp fees). The 5$ difference is their processing fee.
@RPietila paid 3.09$ and got to enjoy a bottle of fine wine worth 500$. He has the same amount of bitcoins that he would have if he did not buy those 1.03 BTC way then.
@JayJuanGee paid 525$ for the privilege of paying the rest of @Rpietila's wine bill (496.91$), plus three bank transfer fees, the Bitstamp trading fee, and the Bitpay processing fee; but he now has 1.03 BTC more in his hoard, nominally worth 515$, that he may be able to sell to @Erdogan tomorrow and thus pass that privilege on to him.
WITHOUT GOING THROUGH BITCOIN
@Rpietila clicks the bank payment option and gets the wine merchant's bank account #.
@RPietila sends 500$ to that account, pays a bank transfer fee of 5$.
NET RESULT:
@RPietila paid 505$ and got to enjoy a bottle of fine wine worth 500$.
CONCLUSION: Left as an exercise.
You forget Years ago, the price of a fine wine worth $50, and it's the fact it now costs $500, that we all want Bitcoin. Bitpay, are just working on ways to get you to spend your bitcoins nothing more nothing less, and they have to make a profit doing it or they'll disappear.