Why are they using a relay in the first place? The gain switching happens at a low-impedance node behind the differential stage. An analog CMOS switch would be perfectly fine for the job at less power, size and less cost...
Cheers
Andreas
Analogue switches have some serial resistance. This is also function of the signal being switched. It also has some input capacitance, so you cannot "just increase the feedback resistance" to get rid of this. It's not like it is impossible to solve these issues, but I'm not surprised if the designer doesn't want to deal with them, and decides to use a simpler method that doesn't have these issues.
There's less to deal with than one might at first think. Figures for the 74HC4053 analog switch (3PDT), which I just happen to have a data sheet handy for: input capacitance 3.5pF, ON resistance 100 , ON resistance mismatch between switches 9 . The THS4631 input amplifier has an input capacitance of 3.9pF and that's in the high impedance zone so 3.5pF in the low impedance zone isn't going to be a problem.
It's as well to remember that the original purpose of the venerable 4066 before people started using them to switch pukka analogue signals around was to switch high speed digital signals around, copying from the IC design technique of building multiplexers and the like from pass transistors rather than from gates. These aren't low frequency components.
I'd use a slightly different topology if I was to use analogue switches, there are little tricks to putting them in places where their resistance (and more importantly the non-linearity of that resistance) has little effect - think "switch currents not voltages".
I don't think the designer was necessarily looking to minimise the work they had to do - adding a whole microprocessor sounds like unwanted/unnecessary complexity to me. As to choosing a latching relay over active switching, perhaps the designer is, like me, a latching relay fanboy. I however avoid the single coil versions to avoid having to mess around with reversing the coil polarity.
I had my fair share of designs with analogue switches. Probably my favourite is the ADG5408 and 9, that solve that nasty latch-up issue for inputs.
While you can use different topologies, buffer opamps (which don't get overloaded, when switching their input) and others, as I said, maybe the designer just didn't want to deal with the design complexities.
Maybe they had to put a microcontroller on it. I had a design like that, I finished it, presented it. They asked how much Firmware work do I estimate, I said 0, there is no microcontroller on it. I solved the task at hand with a couple of logic gates.
I had to go back and replace those with a micro, so it can be programmed, "Just in case they want to change the functionality"
One other explanation is the lack of clean sheet design. Totally imaginable, they had to start with an existing topology, and only replace the mechanical switch, and couldn't rearrange the opamps to get a better product.