It's not like you should focus any support though. Beside Soraka. She remains exception for pretty much everything.
Tanky supports are ignored, because they are tanky, and beating the ADC is more important. They still has their uses, but since tank nerf they are worthless in later stages. Unless enemy is seriously stupid.
Poker supports are just another laner. In lane phase they should only be focused for all-in, because you aren't able to stop their combo in most cases, and once that's over their damage will be drastically reduced. ADC on the other hand will do it's damage constantly. After midgame they should get the attention depending on how fed they are, and in lategame you focus them the same way you focus any DPS.
Protectors can also be ignored in most cases. Lulu, Nami, and Janna can defend themselves the same way they defend their ADC, and while they sacrifice some buffs in doing so they make you use your time and CD on them instead of the guy who destroys you. Yuumi can be ignored, because you don't have a choice.
And there is Soraka. If not countered, then easily the most powerful support since rework. And if enemy can focus, and buy heal reduction, then nothing special. Even better counterplay is to focus her directly. Since her self heal is much less, than her heal to others.
Now think about it for a second. If Yuumi were a usual protector with usual health, and being targetable. Would it worth focusing her? The answer is no. Her healing is not so ridicilously big as Soraka, and she can heal herself for the same value. If Yuumi stands close to the ADC, then getting the ADC first would be still better.
Now here comes Yuumi's "power". The ability to heal frontliners without being targeted. Well there are 2 type of them.
Pure tanks should be ignored at all times. With or without supports. Unless you fight against them only this isn't really a problem since you should focus someone else. If tank takes no damage, then there is nothing to heal. You gona beat it when teammates are gone in 2v4.
Damage dealers stands above priority over supports. They kick your ass while you kill the support. Just like an ADC.
Yuumi has 2 big problem in my view.
- Extreme sustain. This part gets solved, but here mana gain from passive made her able to heal the carry, and poke forever. Something other supports couldn't do. Well maybe except Bard, but he has other strong weaknesses.
- Her ult has way too low CD compared to it's power.
To be honest supports in general are too weak since forever compared to other roles. The only support who is strong enough to get any attention is Soraka. All other can be neglected.