One word: chargebacks.
The main disadvantage with taking card payments is that clients can then report that it wasn't them / some other fraud. If the card company believes them - and they tend to do so, because there are more customers than people accepting cards - they get their money back and you get the money taken off you, typically with an additional charge for being so silly / guilty for accepting a fraudulent transaction.
If the card company discovers what's actually happening (for example, because someone does fancy a freebie via a chargeback) then they are very very likely to be annoyed. None of the main companies want to take payments for sex work and those that do will charge a hefty premium. When banks get annoyed with you, you can easily end up with no-one willing to let you have a current account.
If you're determined to try, Square aren't owned by PayPal in the way that iZettle is - PayPal really hate sex work - but there's a reason that sex workers aren't like performers at the Edinburgh PBH Free Fringe, all clutching their card readers...