Saying that all enchanters have no counterplay is pretty bold as I'm willing to argue that they do for the most part as name and taric are both enchanters and they both have pretty good counterplay.
Soraka suffers from a 800g item that basically perma reduces her effectiveness by 40% and her laning phase is punishable by dodgeing her Qs and trading on her when she misses and goes for them or force her into a passive style which nets lane priority and pressure for u against the soraka lane if u know what ur doing.
Janna suffers from she has basically no laning phase after the double hotfix as her shields a ghetto lulu shield she does no damage so pushing the enemy for having a janna lane isn't hard which should net u advantages which u can carry throughout the game.
Nami her bubble isn't the easiest thing to land and a lot of her power budget in her R and Q makes her have counterplay in the fact that u can dodge both.
Karma actually is interactive early as shes a lane bully and then she suffers late due to having 1 spell basically as support so she falls off.
Taric his ult has a time window which is telegraphed and suffers from being weak to disengage and cc or burst and his E which holds most of his power budget out of r is a telegraphed delayed skillshot.
Sona is squishy so shes easy to punish with CC or burst
Enchanters as a class are not the issue its how power budget is distributed within there kits example being soraka who has basically all her power in just healing and her W or sup karma who has all her power really in her mantra E if it was more evenly distributed between all 4 abilities and passive theyd be less frustrating and have more room for skill expression. Another problem with enchanters is that as a class are very item dependent when power should be pulled from the items and placed into the kits of the champions themselves to add more uniqueness between them rather then all of them being walking effective gold bots late game for the most part, name is a good example of what an enchanter should look like she has cc peel some healing and a passive that she can get creative with. Making them a 2nd class support makes 0 sense as we already have a ton of champions that are in the dirt destroying the class isn't healthy for the game and doesn't solve anything.
P.S. ur ivern examples a tad flawed as he was good due to how he interacted in the jungle and how good daisy was for sieging and controlling objectives his shield was basically all his power out of basic abilities and even still wasn't what made him good.