One specialized application where alkalines are recommended is in avalanche transceiver beacons.

Most modern beacons have a charge indicator. When mine gets below about 80% I change batteries. The problem with rechargeable batteries is that they have a very steep decline curve as they approach the end of a charge. Alkaline batteries have a much more gradual decline of charge over time.

It would not be a good day, if you start a ski tour with your beacon showing a healthy charge, only to have it fall off about the time you or someone in your party get caught in a slide. If someone in your party is buried, and your beacon dies, you don't want to be wasting precious moments changing batteries so you can search for them. If you are the one buried, and your beacon dies, you will likely die too.

For more information on transceiver batteries see Avalanche Beacon Review - Batteries.
To compare batteries, see Battery Test Comparator