The existence of introns in mrna-encoding genes seems to be a problem because so much cellular energy goes into splicing them out during transcription. what is one benefit of their presence in eukaryotic cells?

In normal conditions, introns serve following functions in the body of an organism:

1) They contain genes of miRNA which are known as Mirtrons, reverse transcriptase, endonucleases, transposase etc.

2) It is because of presence of introns that alternative splicing of mRNA is possible. The sex determination in drosophila is based on alternative splicing.

Apart from this, alternative splicing can be useful and beneficial in an unforeseen situation such as an environmental problem which is faced by the organism for the first time.

Explanation:

Alternative splicing is an important mechanism because with the help of alternative splicing different type of proteins can be synthesized from the same pre mRNA transcript. In case suddenly the surrounding environment of an organism is changed and the environmental conditions have become extremely harsh due to which organism's life is at stake, in such situation organism may make a different type of protein through alternative splicing which can help the organism in survival.  

Default splicing in Drosophila leads to the development of male off-spring while female off-spring is produced as a result of alternative splicing.  

555555555555555555555555555555555555555555555555555555555555555555555555

there are so many examples for that in different areas, like biology experiment carried out in our lab recently.

here's one link: