CAN: Difference between an MCU with CAN embedded peripherals and one that does not?
You can avoid a lot of confusion if you get your terminology right.

To access CAN bus the MCU needs two things: CAN Controller and CAN Transceiver.
Controller has Tx and Rx pins. Transceiver converts these pins into CANL and CANH bus signals.

When you say "MCU with CAN embedded" what you really mean is that CAN Controller is already part of MCU, so you only need external Transceiver (e.g. MCP2551) to make it work.

When MCU does not have embedded controller it needs both external Controller (e.g. MCP2515) and a Transceiver.

Finally, when people say "adapter" they usually mean external device that has both Controller and Transceiver on one board.

Note that MCP2515 is not an "adapter", just like MCP2551 is not a "converter".

So, to your actual question:


  Why can't any MCU with tx and rx pins use just one signal converter?
  Why does this also need an adapter?


the answer is: MCU with embedded CAN controller does NOT need an adapter.

However "any MCU with tx and rx pins" does not describe such an MCU, because having Tx and Rx pins is too ambiguous, it can refer to UART interface, for example.