The problem is that Nintendo is taking down fan-made games that would, if anything, benefit them. Instead, they opt to take the role of a bully. They have the right to that, but they also have to face the backslash because people have the right to get angry about Nintendo's actions. All in all, Nintendo is not a modern company, and this is just another sign of it.
Most of us misunderstand teh reason for take down notices. There are 3 main reasons.
1. Brand protection. You can't guarantee the quality of a fan game. Poor games can reflect badly upon Nintendo itself as many players may not be aware that Nintendo didn't develop it (see Pokemon Go to understand players being unaware of Nintendo's involvement in a game).
2. Time and money. Any time and money spent on fan games is time and money not spent on official products.
3. Competition for currently marketed products. You don't want to spent millions pushing a game only to have fan made games pulling players away.
To consider the opposite, how well is Sega doing by allowing fans to make Sega based games? Any tangible benefit at all? Do you really think Sega would be OK with a fan based Total War, Yakuza or Phantasy Star game?
I don't think any of these is a real problem.
1. Poor products won't get attention for long, and Nintendo could always just target the poor products instead of every single one. Fan-made products are sort of a niche thing anyway, and I bet that most people familiar with them know they're unofficial anyway. I can see some potential issues with trademarks, but I haven't really heard about that side of the argument much. I'm guessing it's not a huge problem when no one's profiting from the products.
2. Fan-made products are mainly targeted at fans anyway, and fans are probably going to prioritize official products.
3. I don't really see how this is different from #2, so nothing to add here. See my answer to #2.
I think the threats you mentioned are somewhat real, but I don't think any of them is a problem due to the benefits of fan-made products. You get bigger brand recognition for free, might attract new fans, and you end up looking cool when you have a relaxed relationship with fan-made products. On the other hand, it's not good publicity to ban these things, it can make you look anything from bad to evil.
As far as I know, Sega isn't doing too badly. Can't say whether there's any measurable benefit to allowing fan-made products because anyone's even tried to measure it, and it's probably very difficult anyway, but at the very least you gain some good publicity from it. I don't really see how this has harmed Sega. And I suppose bigger products like Total War or Yakuza could be different, but that's mainly because they're pretty huge titles and guaranteed to attract more attention. There, the drawbacks you mentioned could well be significant, but I don't see much point in discussing them because no one's ever going to create anything like that for free (and even if someone does, it's almost guaranteed to be of much lower quality).