In terms of the length of time it takes, this is partially down to ensuring the track isn't full of cars trying to catch the safety car "train" which gives marshals no clear gap to work on whatever brought the SC out in the first place.
Once the incident is clear - and only when it deemed safe to do so by the folks "on the ground" (the Incident Officer and/or Post Chief in the UK), Race Control (chief marshal & Charlie Whiting) & with input from the SC observer - the instruction can be given for lapped cars to pass the SC and proceed at increased (but not full racing) speed to catch back up.
It's all to do with minimising risk. It could be made shorter by waving them through earlier, but that would make it more "exciting" for us lot dealing with things!
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