Each Sutta was intended for a specific audience to address a specific issue. This is one of the reasons why there was a need for an Abhidhamma that consolidated the messages from all of the Suttas into a overarching framework.
You are absolutely correct that each Nikāya has a different "character". The Dīgha Nikāya tends to include a lot of mythological material and complex arguments. The Majjhima Nikāya tends to include clear explanations of fundamental doctrines. Because of these differences, the different Nikāya appeal to different people for different reasons.
I think that it is important to view the Sutta Piṭaka as collections that evolved over hundreds of years. There was no "master compiler" who said, "Okay, let's put that here for this reason...".
Recent scholarship has compared the Pāḷi Suttas with the Sutras from other schools. Schools started to diverge about 100 years after the Buddha's parinibbāna. In general, the core messages contained in the Suttas and the core messages contained in the Sutras are almost the same, suggesting that the core messages predate the split. Some of the details contained in the Suttas and the details contained in the Sutras are different, suggesting that some of the details were added / deleted / changed after the split. In many cases, the organization of the Suttas is different from the organization of the Sutras, suggesting that the final compilation into Nikāya / Āgama was not determined until after the split.
BTW, the Abhidhamma and the Abhidharma are quite different, suggesting that these were not "fully baked" at the time of the split.
So getting back to your main question... I do not believe that the different "character" of each Nikāya was by grand design, it was more "evolution" rather than "creationism" :-)
Actually, the Suttas (MN 22) mention nine ways of presenting the Dhamma:
dialogues (sutta), narratives of mixed prose and verse (geyya), explanations (veyyakaraṇa), verses (gāthā), spontaneous exclamations (udāna), quotations (itivuttaka), birth stories (jātaka), amazing events (abbhutadhamma), question & answer sessions (vedalla)
Looking at this list, it appears to be grouped according to style of presentation rather than by intended audience. Some of these (udāna, itivuttaka and jātaka) ended up being separate texts in the Khuddaka Nikāya.