For me, I have used feudalism and I personally think it's quite cool
There was this one time (monarchy diff, don't remember the civ
) when I was kinda determind to try it out, I knew that my economy couldn't handle Republic (and thus a peaceful option wasn't possible), and because I wasn't really bothered where the game was going. I was playing for the fun of it. Also, I was involved in a lot of wars (closed space, no place to expand) and needed unit support costs to be lower.
So I tried it
Loved it.
Couldn't get enough of it.
I found that I was slaughtering the opposition with huge armies and that I had plenty of money.
Techs weren't so good but because I changed at the beginning of the Middle Ages I was still fighting AI units from the previous Age with a numerical advantage
and before they got themselves sorted I was a huge civ
I was reluctant to change back into another government coz of many people here saying "too many turns of anarchy are bad" and because I knew my economy wouldn't benefit from the change, but I needed to because otherwise I'd fall behind in tech. It's a difficult transition from Feudal to Republic but I managed it and looking back, I should have just continued the military expansion, but too late for that now
Anyway, that's my little story about Feudalism. Personally, it's fun and in games where you're not bothered about what happens, use it because it'll make the game seem that little bit... better in a way. Can't really explain it really
But if you want to beat higher levels and really 'play' the game to win and get a good score, ignore it