Not MOBA's as such but I play other games quite a bit and it is actually good for my creativity. I do creative things when editing gameplay footage, when providing commentary and when coming up with unique things to do in games and unique things to do with gameplay footage. Many but not all games also often require you to work out different solutions and strategies (i.e. to think creatively). YMMV so we probably have different experiences but for me, it is typically good for my creativity. As for the productivity, it depends if I was meant to be doing games or other things I guess... If I'm meant to be making gaming content, it is very productive - if not, but it is my relaxation - it makes me able to be productive by being needed leisure time - but if not and I'm stuck down a wormhole of playing rather than doing other things I need to do, then it is bad for productivity, though then the fault does not lie with the game itself normally anyway.
Its effect on my productivity can vary and is situational but it is definitely a positive for my creativity personally though.
Well my friend some games do help in improving creativity but MOBAs dont help at all they just devour you into thinking you're doing something really important and essential
This is where people lose it