Increased depth creates more exposed surface area on the side of the pans and will lose heat to the ambient cold air. That said, I don't see any noticeable effects of boiling deep. The backside of my pan gets heat leaking through going to the flue so it actually helps me on that side.
I will also mention I'm on thick pans which are slower to respond and retain heat longer (although are less efficient). I don't see why that would change anything with sap depth, but just stating it since many others seem to say they see a difference in depth. I think they're just impatient
2021 - 15 taps
2020 - 20 taps, 2 gallons syrup
2016 - 25 taps, 2.1 gallons syrup
2014 - 14 taps, 1.1 gallons syrup