This depends on the transaction. As escrow is generally a buyer protection, the seller will consider it a 'nice to have', rather than a 'must have', so frequently insist that the buyer pays. In many circumstances, however, both parties recognise the benefits and, a bit like legal fees, agree to split them.
Private escrow accounts provide security, trust and transparency to ongoing or ad-hoc payment requirements.
Third-Party Managed Accounts (TPMA's) are a convenient way to manage complex, high-value or even routine payment operations.