These are side effects of HOW Finns lost variation, and what variation was there in the beginning. This is not result of low variability itself, but impact of what variability was left. Basically inbreeding depression. A very slow population decline could result in quite different end result, more akin to purging less advantageous gene variant combinations out of the population.

Effect of low variability is that the population is slow in adapting genetically (by selection on existing variation). Need to wait for suitable mutations.

Generally, many inherited diseases are adaptations to other environments. I guess the last one I saw, was suggestion that many autoimmune disorders are related to survivability over plague.

[Added: By the way, Finns lack many genetic diseases that are common elsewhere]