the 'Axoloti control board' has another stm chip on it. and yes, its seems quite common to have additional chips to drive displays, and perhaps pots/encoders etc.
(organelle similarly has an stm chip for its display/encoders, which then communicates with the other board containing the A8)
its a good strategy if you want to have more than a few pots etc, or as you say a 'cpu' intensive display... BUT it comes at the expense of having to write a protocol between the Axoloti board and the slave board, be it over I2C/serial/spi... this is fine if your an experienced programmer, but perhaps daunting if your not.
(note: communicating with another board also is IO, so will take resources from Axoloti)
lets consider the above lcd, example, your choices are:
a) connect lcd to Axoloti, convert the Arduino code for Axoloti, then you can immediate create objects accessing it.
b) connect lcd to Arduino, then Arduino to Axoloti... you get the Arduino code for free, but you now have to write code on the Axoloti to send messages to the Arduino, then code on the Arduino to receive and decode these messages... interfacing with your chosen transport i2c/serial/spi
(a) is trivial, so if you just want to write a bit of text, its quick and easy.
however, (b) is more flexible, once the protocol is in place, you can extend it to cover, pots, midi, etc.
(b) also has one other advantage, which I've been interested in recently , it can be platform independent/modular... so your 'controller' might be built initially for use with Axoloti, but could then switch it over to use with (e.g.) Bela. (some level converters may be necessary)
I suspect this may be a simplistic view - Axoloti runs chibios and has its own firmware, so whilst many of the calls are similar they are not identical... code modifications are going to be required, but I don't think they are often going to be difficult/complex.
(lets also bare in mind, source code from the rPI may also be a candidate for 'donor code')
there really is no 'one size fits all' , depends what you want to do , what your skills are... will dictate if you need/want additional hardware, and how you interface to it.
btw: ive just noticed there is an i2c interface board for the 1602A, this has the advantage you only use 2 digitial pins ... I think I'm going to grab one