Exactly.
My collar is a prize not a shame. For us it is our version of a wedding ring.
I have the voices of my past dating world that constantly degrade me for being an escort for 6 months of my life, of all things. Master builds me up, to try and hush all the voices of what a 'proper' or 'good' woman should be, so I can stop feeling ashamed, and hating myself for my sexual, kinky and adventurous side.
If he used it to shame me, I would retreat not lean into it.
For those who understand the mindset of the sub who feels safe in their situation, the leash is an added reminder while in subspace (like mentally releasing, in a cloud) to the surrender of leadership. Domination in its truest form is 80-90 % mental and 10-20 % physical. It is a mental game.
I know it gets used for humiliation kink, it's kind of where the fun is in it for clients. But it has it's many uses.