I do not recommend finishing any tile edge with caulking.
Shower door curb edge finish.
A great and well made shower curb does all that and is fully waterproof.
A good shower curb keeps water contained in the shower area preventing you from soaking the bathroom floor.
Once the mesh is in place it is stapled onto the front bottom edge of the curb and you float the 2 to 3 inch thick layer of finish mud that forms the shower pan which locks the inside section of.
Glass tiles tumbled stone tiles and some porcelain tiles have edges that do not require a separate edge piece.
I think you should tile the whole top and front of the curb.
As you might expect different people use different methods to build shower curbs.
Shower door bottom seal 2 pack glass shower door seal strip shower door seal frameless seal shower door stop shower leaks and create a water barrier 3 8 x 39 2 4 7 out of 5 stars 166 17 88 17.