Online booking or phone bookings?

Should a business take bookings online?

Almost always yes. It captures the bookings that would otherwise need a phone call, at hours nobody is answering, at effectively no marginal cost.

What do booking widgets get wrong?

They cap what they will accept. Party size limits, no option for anything unusual, and no route for a question, so the highest value enquiries are pushed to the phone.

Check what your widget refuses and where those people go. That is where the money is leaking.

Do I still need the phone answered?

If the widget cannot take everything, yes. Otherwise you have optimised the easy half of the problem and left the profitable half unattended.