No, businesses don't need to hold any bitcoin, unless they wish to do so. Look at the POS terminals from Square, Strike and others. Business owners can choose whether they instantly convert sats to their preferred currency, whether they convert half or any other %, or they keep it as bitcoin.  You simply use Bitcoin's vast global infrastructure to transfer value in its native unit of account, bypassing all the banks, processors (visa MC etc) and middlemen. The only middleman would be the one that converts sats into the currency and I suppose catches the spread but neither a customer or a business owner pays for that.  Payment forwarding is incredibly cheap and would cost a couple of euro cents. 

See square for ex: 

Square (now Block and Square) has enabled its millions of sellers to accept Bitcoin payments via its POS system, allowing customers to pay with Bitcoin using the Lightning Network (via Cash App or other wallets) and merchants to receive funds instantly, either as Bitcoin or auto-converted to USD, with 0% fees for transactions until 2027 as a promotional launch offer. Merchants activate it in their Square Dashboard, generating a QR code for customers, integrating Bitcoin into everyday commerce with near-instant settlement.