Absolutely not.   For a buyer to demand THE escrow is absurd.  If that were the case, then any scammer would simply select themselves as escrow.  Might as well simply demand the seller ship first prior to any payment or demand they accept an IOU, bad check, stolen credit card, hacked bank account, or hijacked paypal.

The seller is the one to select the escrow and/or gives various escrow options and let the buyer select from that.  Agreed that both should be comfortable with the choice should escrow even be needed.