Nathan, I'll give you the short version first and the long version after: for your particular combination, a regular examination by someone who does them all day is one of the few add-ons on the whole menu where the arithmetic is on your side. For dgb it was paperwork. For you it is not.
The reason the two of you get different answers is that this is one of the screens where the evidence bodies specifically have NOT said "everyone, every year". When the U.S. Preventive Services Task Force looked again in 2023 they concluded there is not enough evidence to say whether checking symptom-free adults across the board does more good than harm, and that is why nobody sends the whole population an invitation at 50 the way they do for bowel screening. What the same evidence is clear about is who carries the risk, and you have just described most of the list: a high mole count (more than about 50 is the number that gets used), skin that burns rather than tans, blistering sunburn in childhood, and a first-degree relative with melanoma. Any one of those is worth mentioning to a clinician. You have four. That is the group dermatologists commonly see on a schedule, and it is the group where the annual check stops being an upsell.
On mole mapping. Total-body photography is genuinely useful for exactly one reason: with sixty moles nobody, including a dermatologist, can remember what each one looked like last year, and change is the thing that matters most. The photos turn "does this look wrong" into "is this new or different", which is a much easier question. For dgb, with fifteen moles, they are just photos. For you they're the point. What I'd check before paying is that the examination itself is done with a dermatoscope (the little polarised magnifier), because that's what improves accuracy, and that the same service will hold the images and compare them next year rather than starting from scratch.
On what happens when they find one. Usually it comes off under local anaesthetic and goes to a laboratory, and you wait a week or two for a pathologist, and most of the time it is benign, which is the expected result of a careful examiner and not a sign the check was pointless. Fi's two scars are what that looks like in practice.
I wrote up the whole question this month, including the uncomfortable bit about overdiagnosis of very thin melanomas, in the guide to skin cancer screening and mole checks. The one thing I'd add from my own history: the mole I "kept an eye on" for ten years after my blood pressure scare turned out to be nothing, but keeping an eye on it had meant never actually looking. Between checks, look. Once a month, whole skin, and the mole that doesn't match the others is the one to show someone, whatever it scores on the ABCDE list. And if anything changes before the next appointment, that's not a screening question any more, that's an appointment now.
I'm not a clinician, so how often you need seeing and by whom is your dermatologist's call, and they may well say yearly is more than you need or less. Your dad's history is worth taking with you in writing, because the type and thickness of his melanoma is part of your risk picture too.