Your main question was answered well by
@JohnnyC , so I'll not repeat his points, but I'll venture to add a few thoughts of my own. (Mine are based on a Shearwater Perdix AI because that's what I dive.)
re: which tank pressure displays where -- The transmitter-to-display pairings on all dive computers are constant and unchanging. On my Perdix, the tank readouts are labeled T1 and T2; pairing the transmitters to the computer locks those T1/T2 associations. Unless the computer breaks, the left tank pressure will always show up on T1 and the right tank pressure will always show up on T2. (And if the computer breaks, I've got bigger problems.)
The human factor (i.e., putting the wrong transmitter on the wrong tank) is also not a problem because sidemount diving requires different first-stage-and-hose setups on the left and right tanks. Since I can't mistakenly swap the first stages and the attached transmitters, my left tank will always have the T1 transmitter, and my right tank will always have the T2 transmitter.
re: checking tank pressures frequently -- When tank pressures are off by about 500 psi, side-to-side tilt becomes highly noticeable; thus, a sidemount diver needs to swap second-stage regulators frequently. My SM instructor recommended swapping every 400 psi. Also, because of that frequency, being able to check pressures with minimal effort becomes important, and my Perdix makes that a breeze because the display is always lit up. An SPG, on the other hand, has no inherent luminosity, and an SPG's face needs charging with a light before it's readable in the dark.