You can reach 5k mmr on any hero in the pool if you are good enough at dota/that hero. Its important to understand this intellectually because people get into the habit of saying that a pick is bad or a hero is incapable. A 5k player in a 1k game can win that game on any of the heroes in the cast with an almost guaranteed 100% winrate.
The reason why you shouldn't play a "professional" support has been elaborated above, you don't have professional cores. The second issue when people play support is that I believe there is a general poor ability of players to judge how good or bad they played (support) in any given game as it isn't necessarily one displayed on the scoreboard. When people pick support and lose at lower tiers blaming the cores is the easiest scapegoat. The truth is no matter how good you play support in the first 20 minutes of a game you still need your cores to end it in a matchmade game and dota always allows players to throw until the last moment. Vetting your own performance honestly in such games is difficult to do.
A player might tell their self that they bought wards, they pulled (at least once), they stacked (at least once), they got a few runes. When they lose they might say "What more can I do my carry only had x last hits he was a bad." The truth is if players aren't being anal about small details when on support, its no different than being a terrible CS'er on a core. When pulling, what % of the jungle creeps are cs'd successfully? Is the player controlling the lane dynamic through pulling or just doing it to do it? Contesting every rune? How much time wasted standing around? Under leveled, if so why? Did weak enemy lanes get successfully zoned/denied xp? Did ward placements allow the team to make some kind of play? (Such as a vision ward revealing an uphill area that allowed your team to win a fight because you could see perfectly and the enemy team could be fogged or juked due to lack of vision.) Supports have item timings too (blinks, glimmers to save etc). When people play support they rarely say things like "I had 3 waves of freefarm at minute 8, and I got 1 of 12 possible last hits while my carry returned to lane". If you were 5k at supporting that value needs to approach 12, just the same as if you are a core at 5k that number has to approach 12 also.
People are mentally traumatized by support games where they perceive that they played out of their mind and still lost. If I was going to pick support in a 1k game with my personal skill level - that game plays very different than when I play support in my own bracket. In the 1k game I would be last hitting lanes that my cores abandon with tp scrolls they won't have (also the xp). I would be building greedier items and depending on the hero perhaps semicarry items that will empower my team into the late game, I will be looking to countergank with tps or to join in when my 1k teammates actually group up to push. I will be placing wards to facilitate my own play first - any benefit to the team is secondary to enabling what I want the vision for myself. For example if I want to take a tower, I'm going to ward around that tower to facilitate its killing. I don't care if my carry sees ganks go into his own jungle because he won't notice anyways. Mechanics underlay all of this and my networth will scale to my skill in a sense relative to my opponents. Outside of the fact its an item slot, I can still buy every vision ward in a 1k game and lead net worth easily, and I'm so much worse than the pros. EX. Start as support Lina, Dominate the 1k offlane with my range harassment. Go bottle to use runes, and stack jungle as i collect them. When I hit level 6 I get a kill and when I hit 7 I farm my stacks. I get a quick euls and I will be able to kill a 1k player 100% of the time every cooldown because they will not be able to avoid my movements as they can't even move yet with precision themselves. As you go up in MMR time compresses, A 40 minute radiance Spectre will likely win you a great many 1k games, but signal a loss in anything above maybe 3.5k.
The mechanics are the foundation of Dota, support gives you less opportunity to practice some of them (last hitting) and more to practice others (hit trading, zoning melees, kiting with brown boots). Last hitting has a direct correlation to winning for a very long time. It is easy to quantify in a win and loss, and it has a very binary practice outcome. If you want to improve as a support, you have to be able to judge and vet your own performance on a variety of tiny details that may or may not lead directly to winning or losing. But if you can't understand what you're failing to do its hard to get better at it.
My last point: It is much harder to practice new roles/heroes as you gain more specialist skill set in solo queue. For example if all you do is play mid - if you are a 4k mid, you won't be a 1k support - you have mechanics of a 4k, but you may play a wicked 3.3 or 3.5k support. That's enough of an MMR difference in individual hero pool that you can literally lose a 4k game while playing support in the first 10 minutes and have a very hard learning curve to get some of those more esoteric support details. This story also reinforces the "I only win when I carry." storyline.