Why there is no clutch in gearless scooter?

The concept of transmission is similar in both geared and gearless vehicles. The difference lies in how transmission works. In geared vehicles, we need to manually shift the gears, while in gearless ones the engine itself does it automatically.
The gearless vehicles use what is known as CVT - Continuously Variable Transmission. CVT changes the ratios continually to provide the required torque. The CVT has a system of a pair pulleys of which one is at the front and one at the rear. The pulleys have a set of gears that get activated by the opening and closing of the pulleys. As you accelerate the rear halves of the pulleys open and the front halves begin to close thus activating the gears in a continuous fashion.
The task of opening and closing the respective halves of the pulleys is handled by Aviator. The Aviator is a metal disc that has a metal cage like structure around it with heavy weight rollers. The centrifugal force makes the rollers move out when the Aviator revolves faster as the vehicle is accelerated. Thus the Aviator moves up the shaft and activates the closing and opening of the pulley halves.
The above description provides the basic working of how transmission system works in gearless vehicles. There are many technical aspects involved in properly understanding the principles which are beyond the scope of this response. You may refer to the sites dealing with automotive technology for a more intensive explanation.

The functionality that makes the gearless vehicles transmission possible is known as CVT(Continuously Variable Transmission.). This functionality does the work for keeping the engine running while the bike is not in motion. As explained earlier, it has some benefits at the cost of the fuel economy.

When it comes to the gearless bikes, the functionality is done such as the bike runs on constant RPM. And there is no manual control over the RPM. Here the Continuously Variable Transmission makes use of the automatic adjustment of speed with pulley. It makes hassle-free driving with gear-less but at the expense of fuel. The more it stops without keeping engine running the more fuel it will consume to fire up and keeping the RPM steady. This results in the limit of how much mileage a bike can give with this lack of control. Also it can affect how much pickup it can take compared to the geared vehicles.

In case of geared vehicles, the clutch is used to disconnect the engine from wheels. Here RPM is controlled with the gears. The fuel consumption is reduced due to manual control over the RPM. And here the pickup is improved. Also the bike when needs to stop, requires the use of clutch or the break. If used, it can stop the bike and fuel consumption to fireup the bike, is relatively less. This shows up in the mileage and overall fuel consumption of the geared bike. There is a power loss during the state that requires up for the CVT and clutch but compared to gearless bikes, less fuel is consumed. This is where the role of clutch is important for geared vehicles.

The variator system usually works for doing the work of clutch for adjusting the RPM apart from the CVT system.