Be careful saying "it seems ... relatively easy" in relation to an open source project, because people are likely to turn round and say "well if you think it is so easy, why don't you write the code and submit a patch"
The issues is now Moodle stores the data about what is in the quiz. A particular question added at quiz editing time is stored one way. A random question added now, to represent a question selected randomly when the student clicks Start attempt is another.
However, your guess is about right. It would not be very hard to code up an option like you want. However, I won't get time to implement anything like that for the foreseeable future. It will require someone else with the time and inclication to write the code for it to happen.
I will also point out: It is right be concerned about fairness with random selection made at run-time. However that is one of the things that the Statistics report is designed to help with. It will show you all the different questions that students saw in a particular position in the quiz, with statistics like the average score they got. Therefore, you can verify that the different questions were roughly equivalently difficult (or make a manual adjustment).