Should I give my Beetles to Beedle?
15 Electric Rhino Beetles are used for upgrading some particular pieces of equipment. See below for end game spoilers:
The 'of the Wild' armour set, unlocked by completing all 120 Shrines.
Other than that, there are no other uses for Beetles. So feel free to give them to Beedle to make him happy, or keep them for making elixirs. The reward from Beedle doesn't improve beyond a relatively low strength Mighty Elixir.
Hold on to them. They can be used to make some really good elixirs. Particularly the electric rhino beetle. Keep them for sure!