Why is the license plate blurry in the camera's live view or recording?

Consumer-grade CCTV cameras are intended to be used for general surveillance like capturing people or animals through PIR and motion detection and recording, facial recognition (if any), or other types of detection. They are not equipped with the same hardware capability and specifications as a number plate capture camera or a number plate recognition camera.

Reason 1: Misconceptions about resolution and wider-angle

A high resolution or wider-angle does not have the ability to read license plates from afar. Most consumer-grade cameras at 1080p can make the license plate visible if the car is within 6 metres or so, which is often not enough distance to reach from where the camera is mounted to the road. As for wider-angle, the field of view is broader but sees less farther.

Higher resolution 4K cameras capture more details up to a certain distance as there are more pixels. 
However, if the plate was further away, the 4K quality with a standard 2.8mm lens wouldn't have been enough to read it. This is generally why you would want to use greater lens for license plate capture, such as 12mm.

Reason 2: Shutter rate (confused with frame rate)

A security camera with high frame rate may give you more opportunities to get a good shot, especially with fast-moving vehicles. However, it is nowhere near as important as having a high shutter rate.

Most consumer-grade CCTV camera lens are below the minimum requirement to make text or license plates look clearer. They have a shutter rate of around 1/20 or 1/30. If the camera does not have the ability to switch shutter rate, it makes them unsuitable for nighttime plate capture of moving vehicles. Number plate recognition cameras can have a shutter rate of at least 1/250. To capture plates at night you will want a shutter rate of around 1/1000 to 1/4000. This comes with the trade-off of darker pictures of the whole camera view.

Certain Swann NHD cameras have the ability to adjust shutter rate and can be optimized to enhance the view of text up to a certain distance. See Why do moving objects blur and how to correct this?

Reason 3: Night vision

If a camera does use a high frame rate and can capture plates during the day, this will not be true at night. A camera with an automatic or static shutter rate will not be able to properly compensate for plate capture at night while the camera's infrared LEDs are active. Night vision security cameras have too much IR light which creates a bright reflection, or glare on a license plate. 

Reason 4: Video compression

Lossy compression is the main drawback of digital surveillance systems. Very often, the resolution is actually pretty good, but the compression makes the digits unreadable. Videos are compressed in order to save bandwidth in transmission and space in storage systems.

Reason 5: Viewing angle, distance and height

When capturing license plates, it is crucial to consider the location where the camera is mounted. The camera should be positioned to face approaching or exiting vehicles, ensuring that the viewing angle between the camera lens and plates is no more than 15 degrees in the horizontal or vertical planes. If the camera is mounted too high or too far away to the side, it will not be able to provide a clear view of the plate. For optimal license plate capture, the camera should be looking directly head-on at the path of moving vehicles. However, movement toward and away from the camera is less likely to be picked up by PIR+Motion detection.

When mounting a camera to capture a license plate, it is important to consider the height at which it is mounted. If the camera is mounted too high, it will be looking down at the plate, similar to looking at the top of someone’s head and expecting to see their face. This can create issues where the text on the plate becomes obscured and unreadable. It is easier to read a license plate when the camera is looking directly at it.

Proper automatic number plate cameras make use of fast shutter speed and bigger lenses (at least 12mm) to capture license plate numbers from afar in motion.