Even Mitt using the absolute reference scale draw some power while they are off. Making a latching power circuit is not worth the cost, because they last (per some forum members) up to 6-7 years on a single SR44.
Some of the cheaper calipers draw more sleep current for an obvious reason; they automatically turn on when you move the calipers. They are either doing some ADC reads while off (and this doesn't mean they don't necessarily go to sleep between intermittent reads) or they are set to a comparator/ADC interrupt/wake up... which this also draws some current. The Mit absolute, you have to press the on/off button to turn them on. A digital input interrupt draws less power than a comparator or ADC interrupt. (ADC interrupt is an active thing, really, with sleep in between reads). Any analog input draws more quiescent current than digital. There's also potentially significant difference in sleep current between micros.
That said, with my calipers, an alkaline LR44 will last something like 3 months before it goes on the fritz. Using SR44 silver oxide, same battery that the Mitts ship with, I have gotten over 3 years on a battery. There's no reason to take the battery out when you're not using it, if you don't cheap out on the battery. If you put an alkaline cell in a genuine Mitutoyo, I am sure it would be shitty, too.
Apparently, the fake Mitutoyos which sell for up to $75.00 skimp out to save 10 cents on the battery. The battery package is printed SR44, but it's an alkaline button cell in the package. These are so much cheaper, they apparently include a second LR44 preinstalled in the calipers. The genuine Mitutoyos only come with the one battery. It seems stupid to skimp here, when the difference is so astounding. Nothing using digital logic should be running off a single alkaline; there are silver oxide cells and/or 3V li ion button cells. But if you get frustrated with your calipers 3 months after you bought them, that means you might buy MORE. This is smart. They just need the caliper to impress you long enough to get through a credit card chargeback window.
The silver oxide discharge curve is so flat that silver oxide batteries are sometimes used as a 1.55V reference voltage. Alkalines start out at 1.6V+ and drop fairly linearly to below 0.8V when flat. Look at the minimum voltage requirement for microcontrollers and you see why a single alkaline cell doesn't last long. Even your TV remote takes 2 in series.