Bard I think is a consistently popular support, including for players playing against him. He gives plenty of opportunities to both his allies and opponents, and has a kit that isn't too overly focused on saving allies or stun-locking enemies, so he doesn't feel excessively frustrating even when he's played well.
Nami is another support who's generally well-liked by the Boards. She feels fair to play against, but also satisfying to play, and has a diverse array of tools that, again, lets her assist allies and disable enemies, but without ever shutting someone down completely at the press of a button.
By contrast, the major problem with many of the supports mentioned in the OP is that they frequently have this one button they press that can instantly shut down much more skillful plays. Enchanters typically have this problem due to an excessive portion of their power budget being placed onto on-demand shielding or healing, and particular champions like Lulu, Morgana, Thresh, Blitz, etc. are also notorious for having one CC ability that can easily stop certain champions from playing the game entirely. Mage supports tend to frustrate ADC players because their high bases and relative independence from scalings means they can easily deal a lot of damage in a squishy lane, which feels cheap, and it's especially irritating when these same mages also have damage that is relatively easy to apply, as has been the case for Brand and Malzahar in the past.