The person answering your phone is also checking somebody out
In most single location practices the largest leak is not a page element, it is that the front desk has three jobs at once.
A new patient call is a five to ten minute conversation involving insurance, scheduling and reassurance. It arrives while somebody is collecting a payment, answering a hygienist and signing for a delivery.
Start by measuring it rather than debating it. Almost every phone system will report answer rate, missed calls and time of day. Pull a month and look at where the misses cluster. Lunch and the last hour usually stand out.
Then choose a real fix. A dedicated new patient line, an overflow answering service with a booking script rather than a message pad, or an automatic text back on every missed call so the person who could not get through has somewhere to go.
Whichever you pick, listen to a sample of calls yourself. The call that ends after one uncertain insurance answer, with no time ever offered, is the one worth hearing.