Yeah, I have max skills on my Fire Rakshasa because she's awesome, and because someone early on told me to always get one from the shop every week and save them until I had a creature worth using them on.
I started giving the next devilmons to my Water Sylph, but now I'm debating if I should switch over to my Wind Ninja. I just recently pulled him around the time of the downtime compensation scrolls, and already he's made a huge difference (thanks angelmon dungeons!). My arena offense used to be Fire Rak, Fire Vamp, Light Bearman, and Light Fairy. After being able to move runes around for free, I switched to Fire Rak, Light Bearman, Water Sylph, and Wind Ninja. It killed me giving up the Vamp and the Fairy, because they both have fantastic skills, but the overall power of the team seems to have gone way up, and the color diversity helps a lot as well. I'm now getting into the mid-1600s and still winning more than I'm losing...not that it matters much for my reward of course.
I should probably stick with feeding my devilmons to the Sylph to get the faster cooldowns on the ae stuff, and I think that's what I'll do, but man I love that Ninja. I honestly think he'll be my next 6*.
As far as the 4* vs 3* argument...if it is a really good 4*, sometimes there is just no comparison even if on paper they seem better. I don't know much about the DK because I only have the crappy one, but I think there is no comparison between it and some of your other good ones and something like a max skill Inugami. Sure I occasionally get hit with a bad streak from an Inugami, but I'm way more likely to lose in the arena to some 4*. If I see an Inugami on the opponent's team I don't even bat an eye. Stats are typically higher on a 4* too, so runes help even that much more.
Don't get me wrong, there is a time and a place for those 3* monsters, definitely. I wouldn't be where I am now without my Water Warbear and Fire Inugami. And I'll always keep them on my roster for certain things they are better at. But once you get a few decent 4*s, they probably should take a back seat.