If the tips of the fins were only 20 C cooler, then nobody would use them.
That is a misconception.
Newton's law states that :
-----Q = h x A x (Ts - Tamb)
h being the heat transfer coefficient, A the surface area , Ts the surface temperature and Tamb the ambient temperature.
Now consider two surfaces of the same amount of area, the first surface at the bottom of the fin, the second at the top.
If the temperature at the top of the fin is lower then at the bottom of the fin, Qtop will be lower then Qbottom.
If the temperature at the top of the fin is equal to the temperature at the bottom of the fin then Qtop will be equal to Qbottom.
In the last case where the temperatures at the bottom and the top are equal Qtop + Qbottom will be larger then when the temperature at the tip is lower then that at the bottom.
Otherwise stated, the convected heat transfer of the fin becomes better if the temperature drop between bottom of the fin and top of the fin is smaller.
That is one of the reasons why fins in heat exchangers are made of materials with good thermal conductivity such as aluminum and copper. The good thermal conductivity keeps the temperature difference between top and bottom of the fin as small as possible. The other reason being that heat transfer from the base into the fin is large.
More important factors for a good conductive heat transfer are a high heat transfer coefficient and a high surface area.
Radiant heat transfer is the dominant heat transfer mode, over around 750 C. Below that rough temperature, convection does the bulk, and fins are the primary convection improver.
Agreed that at higher temperatures radiation is dominant for heat transfer.
At lower temperatures it depends on the way how the heat is exchanged. With larger fins (fin height 3 cm) there is good conductive heat transfer and less good radiated heat transfer due to the fins largely blocking the radiation.
For the Lugano fins, which have only a small height and where radiation is less blocked and due to the small surface area convective heat transfer is limited. As a result even at the temperatures of about 450 degree C, the radiated heat transfer is still dominant. (See Lugano dummy run data)