First of all, Dengue is an RNA virus and it does not express a reverse transcriptase (I am guessing you are referring to the false priming phenomenon that occurs from performing RT-PCR looking for Dengue genomes but I fail to see the relevance to an in vivo system). The integration events non-retroviral RNA viruses into the genome are exceedingly rare and represent substantially less than once per billion per year phenomena. Your suggestion that mRNA could enter the nucleus when the envelope is dissolved is accurate but it fundamentally ignores that as this is occurring, the DNA in question has condensed into its densest heterochromatic state possible, which would represent a substantial barrier to the integration of any DNA sequence that an intracellular reverse transcriptase would be able to produce.

RNases did indeed likely evolve as an antiviral defense. Nonetheless, they are not the subject of this post as I had an entire separate post discussing the active degradation of mRNA molecules once inside the cell, which I already mentioned to you.

Lastly, the suggestion that the FDA said anything of the sort to Moderna is absolutely laughable. For one thing, the FDA has approved multiple RNA based therapeutics, with many on the horizon in clinical trials: https://www.nature.com/articles/d41573-020-00078-0

You are also completely disregarding that the mRNA in question reflects a specific stage in the replication cycle of EVERY SINGLE VIRUS in existence (this is indeed what unifies all viruses in the Baltimore criteria). The FDA had no qualms approving replication-competent live viral vaccines like MMRV, which have substantially reduced the burden of covered infections. Are you also protesting these vaccines for their potential to alter your DNA? Because I would have to say, you’re going to hate to find out how much more RNA you produce in the course of a true viral infection compared with an attenuated viral vaccine, let alone a conventional mRNA vaccine with no replicative potential. The reality is that there's almost nothing about this technology that is novel other than the name. Scientists simply singled out a particular stage in the life cycle that retains immunogenicity while being unable to generate functional viral particles and their associated disease state.