A third layers , at least to me , seems a bit much. Moving between three different layers. I thought lightning was private in and of itself?
Discussion
You want to use different layers for different things. For example if you need to make a huge transaction you probably care less about speed and it would probably be something to do on layer one. If It's smaller transactions you can benefit from the speed of layer 2. Layer 3 has other benefits and drawbacks. It's up to the user which one to use.
What's the use case for going through all layers at once? I don't see any. Usually swapping between 1 to another layer is enough
LN payments decouple from the blockchain but have not perfect privacy at all.
Ecash aims to a completly different level of privacy.
Different tools for different pourposes, what seems too much today can priceless tomorrow.