Why doesn't mobile esim support SMS service?

Because mobile does not add esim services.

The principle of eSIM card is to embed the traditional SIM card directly into the device chip, rather than adding it to the device as an independent detachable component. Users don't need to insert a physical SIM card, just like PHS in the early years. It should be pointed out that this practice will allow users to choose carrier packages more flexibly, or change carriers at any time without unlocking devices or buying new devices. This undoubtedly reduces consumers' dependence on operators, and operators cannot bind users by changing numbers and networks. Therefore, although eSIM technology is mature now, its current development in China is not ideal.