There are two cases not mentioned:

The first is when you want a detectable loss in performance prior to the total loss of performance. With NiMH batteries, the voltage remains large constant until the end of the battery life, then experience a rapid drop in voltage. Alkalines have a noticeable loss of voltage over the life of the battery. Normally the constant voltage is preferred, but there's not a lot of warning when it dies requiring you to carry spares. This can come as a very unpleasant surprise when using regulated devices like the current generation of pocket lights.

The second is that even with LSD NiMH batteries, the storage life is considerably less then the current generation alkaline batteries. The alkaline will last 5-10 years (in the package) before losing the same capacity as the rechargeable lose in 1 year. For an emergency kit, where you may not be inclined to top off the kit batteries every 6-12 months, alkaline are a the best cost/performance choice.