Averages can be misleading, to be sure. You talk about “average person” exposing 30 people and being unable to identify 6 of them. In order to have an infected person in the group of 6, the “average person” would have had to infect 5 total people. Twice R0. To keep the averages working out, someone else needs to infect 0 other people. In other words, this can’t continue on indefinitely, where each new infectious person can’t then infect 5 more people, 1 or more who are untraceable. That would make R0 5, not 2.5.
In other words, in a specific case, your numbers are reasonable. As a population average, it doesn’t. When you take the population as a whole, the average needs to be 2.5. Your example of how 1 person can infect 10 others, those 10 others never spread it to anyone else, so that path dies and it doesn’t matter we can’t trace 2 of them.