The problem I see is that there is no SAFT in AAA size. The SAFT is 3.7V, instead of the 1.5V of an alkaline. It's higher energy density and that's why it lasts so much longer than an alkaline in a Perdix.
Since there is not a AAA SAFT, that means that a pared-down Perdix that took a AAA battery would get a LOT less runtime than what you can get out of a full-size Perdix (with a SAFT). When battery changes become required that frequently, well, I'd rather have a rechargeable... I mean, it could require a new battery just as often as a Teric requires being charged.
Another issue is screen tech. Shearwater can get OLED screens for the Teric because they are watch-sized and the OLED screen manufacturer is making huge quantities for smart watches. They can't get Perdix-sized OLED screens. That's why they changed from OLED in the Predator to LCD in the Petrel. And why you basically can't get a flooded Predator fixed anymore. They can't get those screens anymore. They don't buy enough quantity for any of the screen makers to make them their own run of OLED screens for a Perdix format. At least, they can't get them, or the price would be unfeasible because the total quantity would be too low. With the Teric, they are piggy-backing off the demand from other industries to get a high quality, affordable display.
And the problem with a smaller Perdix that has a smaller battery, but still has an LCD screen, is that it's a battery hog to run the LCD versus what it takes to run the OLED on the Teric. So, they really just can't go TOO small with that battery or it won't have acceptable runtime.
So... how about a bigger, but thinner, Perdix, that uses an AMOLED screen that is also sourced for some popular smartphone? With a smartphone battery inside. You could have the form factor of an iPhone on your arm - slightly thicker, to accommodate some piezo buttons (that are smaller than the ones on the current Perdix). Plenty of info can be displayed, and the best readability ever in a dive computer. With wireless charging.