Please bear with me as I failed in my brevity check on this one causing my response to be kind of long.
The thing is that Nunu and Singed were roaming so much that people attributed it to abandoning the bot lane. In the few games I watched, it was not like Singed nor Nunu were never present in bot lane for any amount of time. If leaving lane to help ward jungle, help counter jungle, help game is described as "roaming" (which the two cases did in such abundance to fall into the negative/unhealthy/unfun/"I didn't sign up for this category"), then that is precisely what is at issue, and I'm curious where that dividing line is.
However, that being said there are plenty of champions that I simply just find negative to play beside as a teammate. Teemo is one of them. I find the experience pretty much wholely negative, but I've never reported it because it's just a off meta pick (Teemo is definitely NOT meta imo), and it's a tactical difference in playstyle (split push top all day similar to Nasus) and provide 0 teamfight presence. I personally subscribe that team fighting is almost king in LoL and if your champion provides very little then that is a playstyle for which I did not sign up.
I don't necessarily agree that your options A/B/C are the entire sum of options that can be listed. I also curious as to what would be defined as 'unhealthy'. There are a multitude of interpretations to be had with unhealthy. I'm silver, and I see so many people hate and get super irate over the split pushing strategy. I do not get upset. I just do not prefer it in my games personally; Since I am Silver, the chances are that your ineffective use of teleporting and split pushing will be solely detrimental to the team as a whole.
I see these cases as merely people not being used to the strategy and not being able to adapt (probably on both sides). This is what is expected of the Nunu and Singed because the other 4 players will not adapt to their playstyle. Therefore the odd-man-out are expected to adapt in this scenario only to the team, not visa versa.
When I was originally getting on board as Brand Support (support main here), I got a lot of blowback from teammates about the AP support. This is most likely because they do not know how to play with it and do not like it when the low income would potentially get kills due to high base damages and extreme gold : damage ratio efficiency. Luckily for me, since it showed up in pro play, the META itself shifted to that APC Supports were more accepted (and their contributions more understood and how to play with it) and thus I was never presented with the ultimatum from Riot of conform to my teammates playstyles (as it is very different to normal supporting. "The best CC is death") because my choice in what and how I wanted to play was not welcome.
In the end, both Nunu's and Singed's playstyles got the players to Diamond with over 50% win rate which definitely says something about the strat as a whole being effective team support playstyle. It was able to get enough advantages over the other team to make up for an ADC who was frustrated because he / she was 1v2 and has no real developed experience to deal with such a case. It also says that Riot does not allow negative experiences from tactical decision differences to be acceptable. However, following the boards (where people go to whine admittedly), they make a lot of champions that just make you super frustrated and super unhappy to even play against. Riot makes a ton of champions that are oppressive and remain viable so a lot of players are negatively impacted just by their presence in games. This smacks slightly of contradiction to me personally especially when their FAQ on Reporting says (number 3 and 5 for reference) to not ban for off meta selection, nor to ban for tactical decision differences (which I would classify roaming too much under that as it is a tactical choice to do so).
As I list these please know that I am not mentioning these to discuss counter play availability for these honorable mentions, Caitlyn is one such champion for a lot of people. The reason why Blitzcrank will never be strong is because of how completely oppressive his success scenarios are (and I find him to be completely negative to play against especially in lane).
To sum it up, I think that Riot would do well to either rename the role to Bot Support / Bot Carry to help indicate to player that innovation like Singed/Nunu is to be treated with tempered exuberance on the player's part. I was watching Phreak's stream the other day and this situation came up. Phreak mentioned that it is a 'gentlemen's agreement' on how LOL is played that Support is played in bot lane (which again reinforces that it is a META SCENARIO for which you're not supposed to report). Personally, I think a punishment instead of some sort of warning in this case is extreme. Clearly the people knew that their playstyle was making people unhappy, but were misinformed that it was indeed punishable. Riot could have given them warnings instead of actual punishments as they were indeed just trying to play and play to win!