It should come as no surprise that supporting roles or characters in games tend to be the least popular. You could probably attribute this to the fact that they are generally intended to be the most effective behind a wall of teammates and as far away from the action as possible, leaving most of the killing to other people. Overwatch is no exception to this rule, although to Blizzard's credit, they did try and make most of the Support heroes fun to play.
For example, Lucio is typically regarded as the most consistently effective healer in the game, requiring you to simply stand near your teammates to heal them. Similarly, Zenyatta is a very passive healer, possessing a fire and forget healing ability that has no impact on your ability to shoot at people. For people who are new to Overwatch, heroes such as these are relatively forgiving, or at least more so than healers like Ana and Mercy. Despite their fairly passive playstyle, however, Lucio and Zenyatta have not always been the go-to healer combination in Overwatch.
For several weeks, Lucio and Mercy were generally considered to be the best primary/secondary healer combo in Overwatch, primarily because their abilities complemented each other very well; one can heal the whole team at a slow but fairly consistent rate while the other could heal one person at a relatively fast rate and revive people. Meanwhile, Zenyatta was considered to be one of the worst heroes in the game, being easily countered by almost anyone. Lately, however, Zenyatta has skyrocketed to be one of the most consistently used heroes in the game, with sites (and anecdotal evidence) like PlanetOverwatch.org claiming that Zenyatta has a usage rate of greater than 80% within the past week.
Now you may point out that despite all the balancing changes in Overwatch, both Zenyatta and Mercy are relatively untouched since release. The only major difference is that Zenyatta got a little bit more health and it takes longer for Mercy to be able to revive people, so why this sudden shift in attitude? The answer is actually relatively simple: between the removal of Widomaker's ability to instantly kill Zenyatta with a single bodyshot and the inability of random teammates to protect their healers, more and more people realized that Zenyatta is a more logical hero to pick due to how comparatively well-rounded he is.
While both Mercy and Zenyatta have the same health and default movement speed, Zenyatta simply has better abilities. By default, he fires faster moving projectiles that do twice as much damage as a single round from Mercy's sidearm, his healing ability lets him hide pretty much anywhere he wants as long as he can still see the person he is healing, and his ultimate ability makes it virtually impossible to kill him and any teammates that are under its effect. On top of that, neither Zenyatta nor Lucio has to choose between healing and defending themselves, with Zenyatta actively contributing to firefights with his Orb of Discord (which debuffs enemies so that they take 50% more damage from all sources). That in itself gives Zenyatta a fighting chance against most of Overwatch's flankers, not to mention what he can do against large and slow moving heroes like Roadhog or Reinhardt. The only real downside is that his healing ability is somewhat weak, healing at a rate of 30 health per second.
Naturally, Mercy has the best healing abilities in Overwatch (if you disregard Ana's ability to heal 75 health per shot and Lucio's ability to potentially heal 52 health per second per teammate), but they come with so many drawbacks that it is barely worth it. Sure, she can heal people at 50 health per second, but she can barely defend herself (and it comes at a cost of interrupting her healing abilities), her escape ability relies entirely upon teammates, and she is generally considered to be a priority target (even more so than the other healers). Her ultimate ability, while powerful, relies upon the death of teammates and it can leave her entirely exposed in the most dire situations. On top of that, she has to be relatively close to her teammates to heal them and she has a giant beam of light that gives away her position when she is healing someone. While she can buff the damage of a single teammate, it is so comparatively weak that Blizzard has admitted (in one of the early iterations of the Public Test Region) that it might be more effective if she were to pull out her pistol and shoot people instead.
At the end of the day, this means that you are essentially taking the weaknesses of two of Overwatch's most popular Support heroes (low damage and low mobility), ignoring what makes them popular (being reasonably effective at acting independently of the team), and combining all these traits into one hero that is almost always going to be considered a priority target. You could argue that that is the cost of being an easy-to-use hero, but you could just as easily argue that that is no excuse for one hero to be noticeably less effective than the others in a given category.
Now you may ask "Why does it matter if one hero is significantly less effective than the others? Just look at Symmetra, she's borderline useless and she's still in the game." With so many other heroes—especially those that are just as underpowered, if not more so—it may seem a bit odd to focus on any one in particular, but healers are a vital part of any Overwatch team, and it would only make sense to make them all equally viable (or at least equally fun to play as) before all else. Doing so may not make Support heroes popular overnight, but it would certainly go a long way in encouraging people to pick roles that benefit the team more than their own K/D ratio.