Are there fundamental reasons why (exponential) economic growth is highly desirable?
Because according to utility theory: more is better- or at least not worse (nonsatiation- or free disposal).

Your question seems to actually be: why is growth good? 

Firstly, It's axiomatic. Utility theory very formally assumes the law of nonsatiation/free disposal.  Things that result in the death of the cosmos are bad not because we are dead, but because we cannot consume and improve our happiness afterwards. Evidince: We observe that consumption improves happiness.

Second, in cases of limited resources, we have situations where optional growth paths are negative-But this is only because it allows for increased overall consumption.