It’s a good idea.
Adding latching indicators will mean moving up to at least a 64-lead ATmega 1281/2561 with 54 IO lines, or a 100-lead ATmega640/1280/2560 with 86 IO lines.
First, the obvious benefits are that we do away with the LCD shift register (we still have 2 or 4 UART ports, and so may still need to MUX if we go with the 1281/2561) . However, adding the relay latch leds becomes easy, and writing the software is also easier without the multiplexing code.
The costs will be more components, much more difficult PCB routing, and possibly a higher power consumption if we make most of the addition pins available for IO. We might need to re-spec the power supply.
If we decide to stay with the ATmega644, we could show the latch state as a special character in the rightmost space of each line, but this comes at the cost of software complexity.
Which path shall we pick? If we go for a larger MCU, I'd suggest the 2560 - More Flash for bigger programs and 4 UART ports?