Let's use Sona as an example for this. Most sheeple will look at her winrate and claim it to be average or slightly above, but her pickrate in yolo queue somewhat low.
Now let's look at outliers in her winrate: Spellblade and Echo. These are passives you'll be hard-pressed to find on ANY support's top-built items EVER. Is this due to synergy with these items? Decidedly NO. Whilst her winrate with either of these are high, they're only ON-AVERAGE or even below-average with these items' personal winrates overall, they don't work any better on her than any other champion and in-fact performs slightly worse. Why are Spellblade and Echo's winrates so high? Because unlike normal AD/AP items that are reliant on your champ's kit and the other items you build, both of them create a false artificial damage source that is not only independent of your champ and items, but create a brand-new false artificial scaling as well. Buying these items is synonymous to adding a 5th or even 6th skill to your kit.
Back on-track, what happens to our example when these 2 factors are removed from the equation? Her winrate falls below 40%. Let's take this one step further and remove the factor of ranks below Diamond and suddenly her winrate is now all the way below 35%. The conclusion we get from these is that this support character is incapable of performing with only typical support items.
Next let's look at pickrate. In yolo queue, there are 13-15 or more supports with higher pickrates than her and only 6 with lower, even being generous. As a character, she's always been very popular amongst League's fanbase mainly for obvious reasons. She's even attracted a number of non-players to the game through exposure to fanart. Since despite of this she still keeps a very low pickrate, this is NOT the outlying factor. Thus the other main factor is likely the outlier, meaning her perceived strength amongst the playerbase is obscenely low to the point where even diehard fans are unwilling to touch her.
Let's delve even deeper into pickrate by taking a direct look at professional play, across ALL regions. Of any champ picked into the support role, including not only champs typically thought of as "supports," but any picked by a team to be played by their support teammate including things such as Kayle and Syndra. Looking as far back as patch 4.13, she is the LEAST-RECENTLY support to EVER be played in a professional game. We can conclude from this level of play that's main objective is perceived strength that our example's strength is more FACTUAL than just perceived.
I hope I didn't go too off-topic for you. Maybe this example helps better understand what I was explaining.