The booking system usually comes with payments attached
Bundled payments are genuinely convenient — the appointment, the deposit and the sale live in one place. The rate attached to that convenience is frequently well above what the same business could be quoted separately.
The question worth asking is not whether the bundle is easier. It is what the bundle costs you a year, which is a number rather than a preference.
Deposits and no-show fees are a different rate
A deposit taken when the appointment is booked, and a no-show fee charged against a stored card, are both card-not-present. They cost more to accept and they carry chargeback exposure the terminal does not.
If a real share of your revenue arrives that way, it should be quoted explicitly rather than assumed into a single blended number.
You may be able to keep the software
Moving payments does not always mean moving booking systems. Many platforms support more than one payment provider, and keeping the software while changing the payments is often available and rarely offered.