+Fused monsters are often not tradable because unless the person taking the trade knows there stuff they could get stuck with an imperfect monster they were told that was perfect. To be perfect (highest possible stats) a monster needs to be maxed in level. So if someone maxes 1 and not the other the stats might look high enough to have been maxed and there of trick someone with less experience into taking a bad monster.

This I actually like, I just wish there was some way the game could tell the difference on non-max verse max and allow maxed monsters to be traded. That's not going to happen any time soon, but oh well.  

I was talking more about monsters like topaz wolf or the SR that 4 anat turns into. I got a joker warm and an armoured hydra that aren't tradable; they're just rares.  

Derringers chain monsters were tradeable and became non trade after the event where Derringers were daily reward for... makes no sense to me.

Many summoned monsters are non trade, I ended up using my Murder (SR) as fusion food because non tradeable

I understand the + monsters being non trade: you make a commitment to keep it when you fuse+. I understand the invite monsters for a period during and after their related event, but for the rest, it can be really annoying.