So how do you want to implement transmit and receive control logic?

By the way. It takes  about 10 states to implement both.

The example solutions:

• https://www.researchgate.net/publication/280531995_Synthesis_and_Implementation_of_UART_using_VHDL_Code
• http://www.inventus.org/posterous/file/2009/03/192538-alse_uart_us.pdf

Research Synthesis and Implementation of UART using VHDL Code

State diagrams have always been the easiest way to implement all sequential problems and so is the one.

Yes, its better to use state machines to implement sequential circuits.

I think state machine help you to have beater design and in this  condition (serial to parallel and parallel to serial) it's the best way!