The original pilot script for The Umbrella Academy featured Klaus's ability to levitate, but this ultimately ended up being removed (at least, until Ben pulled a Dirty Dancing move on him in season 2). In Gerard Way and Gabriel Bá's original graphic novels, Klaus has the ability to levitate, speak with the deceased, project onto television sets, and speak through radio frequencies, undoubtedly earning his superhero name, "The Séance."
The Umbrella Academy follows seven adopted siblings who were born under unusual circumstances and grew up to have superpowers: Luther (Tom Hopper), Diego (David Castañeda), Allison (Emmy Raver-Lampman), Number 5 (Aidan Gallagher), Ben (Justin H. Min), Klaus (Robert Sheehan), and Vanya (Ellen Page). Sheehan's character is known for his substance abuse issues and for generally being unreliable. Being drunk or high dampens his abilities, so he chooses to be drunk or high most of the time in order to escape the cacophony of ghosts trying to get his attention. As a result, Klaus isn't nearly as powerful in the TV show as he is in the comics.
In The Umbrella Academy comics, Klaus's levitation allows for his character to expand beyond being the most unpredictable out of the seven Hargreeves children. He comes off as somewhat arrogant as he shows off his capabilities inexplicably and at random. The Umbrella Academy season 1's original pilot script is in keeping with this, introducing Klaus as he floats down into the VIP section of a club, describing his look as "David Bowie crossed with Hunter S. Thompson." It's likely that Klaus's ability to levitate ended up being left out of the show because Sheehan's version of the character has rejected his powers, using drugs and alcohol to keep the ghosts at bay. His having such a striking superpower would be at odds with this, and his lack of this innate ability also creates more room for his relationship with his late brother, Ben.
There were only four instances in which Klaus uses his ability to levitate in The Umbrella Academy season 1 pilot, so it was never integral to his overall characterization. Furthermore, his ability to conjure Ben's spirit is far more intriguing and his power of levitation could have detracted from this major plot line. In the comics, Ben does not have the same presence that he does in the Netflix original series. Klaus does not actively attempt to contact his brother, nor does he show an interest in doing so. The entire storyline between the two brothers was created for the series, which makes Klaus an entirely different character than he is in the comics.
Sheehan's character expresses more of a meaningful connection between himself and his siblings in comparison to the comics' version, who does not necessarily want to be bothered by them. Removing his power of levitation takes away one of his biggest character flaws, and also fits with a version of Klaus who is viewed by his whole family as someone who is only capable of messing up. His levitation was amusingly referenced in The Umbrella Academy season 2, when Klaus wows his cult by floating in the air... but only because Ben is holding him up. However, it's possible that Klaus could still learn to levitate for real in The Umbrella Academy season 3 and beyond.
The scene of Ben helping Klaus to levitate can be seen as symbolic of Ben literally lifting him up regardless of the terrible situations they find themselves in. While it was included for comedic affect and his cult story line, it added an extra element that further defined the show's Klaus from the comics' character. But when Klaus spoke to the dead Reginald Hargreeves towards the end of The Umbrella Academy season 1, his father told him that he had barely begun to tap the potential of his powers - which was proven shortly afterwards when Klaus discovered his ability to make ghosts corporeal. If he can learn to do that, then perhaps future episodes of The Umbrella Academy will see him learn how to levitate without Ben's assistance.