NiMH has some negatives compared to alkaline:
Cost effectiveness: on a device that could go 5-10 years on a single set of batteries, selling all of those with rechargeable batteries + charger is going to greatly increase the price. This is especially true if the device is low-cost and more of a disposable type of product (rather than something to be repaired).
Self-discharge/capacity: this has been an issue for quite some time, especially for those of us who have had to deal with that since the dawn of time. You never were quite 100% sure whether the rechargeable cell was going to perform as expected when you grabbed it. A fresh alkaline cell out of the package was a near-guaranteed, known quantity. For the popular NiMH option (eneloops: regular, pro & lite) you must choose between conflicting characteristics of capacity, self discharge rate and cycle life.
Multi-cell configurations: odds are good of having one NiMH cell with a reduced capacity and this means the device doesn't run as long as expected. Unless you're regularly characterizing your cells and binning them by capacity, you are looking at a reduction of the runtime compared to alkaline in addition to the reduced design capacity. This is not insignificant.
Managing NiMH cells on a daily basis: this is not trivial and there are a lot of factors to consider. Just have a look at the official FAQ here:
https://www.panasonic.com/global/energy/products/eneloop/en/lineup/eneloop.htmlSo if you were to sell a device with NiMH and a charger, you now have to explain a lot more to the consumer, and design the device to handle NiMH as well as perhaps alkaline or even lithium.
For alkaline, the big risks for leakage is in a multi-cell configuration, and/or where the device continues to draw power when off. Even when operating, you have a good chance that one cell will fully discharge before the others and the user or the device does not realize this. Then the fully discharged cell may leak if left this way for long periods. This can also happen of course when the device is just sitting and slowly discharges all the cells. One may go dead before the others and leak.
Many alkaline cell manufacturers have made improvements over the years to reduce leakage, and advertise this. There are also a significant number of variables that can impact the health of alkalines, such as the environmental conditions the battery experienced, both during storage and usage. I believe all the manufacturers suggest "cool & dry" when possible.
With that said, I think eneloops in the Fluke 287/289 is a no-brainer, as I mentioned previously.
The BM78x might actually be a reasonable candidate for a lithium-ion pouch cell. Having the low-battery indicator come on at 3.7V doesn't seem too terrible.