Why can't you take a hoverboard on a plane?

Is this a standard text?

Absolutely. Every airline I looked at had such a restriction and I think it's more or less mandated by IATA's restrictions on lithium batteries.

Air Canada: "Small lithium battery-powered vehicles are not accepted in either checked baggage or carry-on baggage due to safety concerns associated to the lithium batteries that power them. Prohibited vehicles include: hoverboards, AirBoards, electric skateboards, airwheels, mini-Segways, balance wheels, battery-assisted bikes and electric scooters. Motorized luggage (e.g. Modobag) is also prohibited."

Air France: "Lithium battery-operated segways, hoverboards, self-balancing hoverboards, Oxboards, electric skateboards, waveboards, motorized baggage (no matter the battery power in Wh and even if the battery has been disconnected or removed)" are not allowed in either checked or carry-on baggage.

British Airways: "Due to the potential fire risk associated with lithium batteries, hoverboards and other self-propelled electrically-powered vehicles such as Air Wheels, Solo Wheels, skateboards, scooters and Hover Karts are completely forbidden."

Japan Airlines: "Personal Movement Devices with Built-in Lithium or Lithium Ion Batteries (Except for battery-powered wheelchairs and mobility aids)" are "prohibited in both carry-on and checked baggage even if the batteries are removed, or those devices sold at the airport duty free shops."

United: "In the interest of safety for our customers and employees, we do not accept hoverboards as checked or carry-on baggage."

Does it have some actual precedent, is it a deliberate allusion to the don't stuff beans up your nose trope, or just a flat-out joke?

It has actual precedent. Hoverboards use high-capacity lithium batteries and such batteries are strictly restricted on flights because they can cause very intense fires if they're damaged, overcharged, undercharged or have manufacturing defects.

At least two cargo flights have crashed because of lithium battery fires: UPS flight 6 and Asiana 991.

Why don't they give something actually realistic as example for the hazards a hoverboard would bring?

Delta don't give examples of why anything else would be dangerous, so why single out hoverboards? It's tough enough getting people to read these things anyway but adding a little essay about each individual item will make the text even longer and guarantee that people won't read it.