In my experience, the children chosen to do things are usually the ones who are capable, show commitment, and often are confident. They also have parents who support bringing them along to practises/rehearsals etc.
It's not nepotism or favouritism, its choosing the best child for the job.
I am not a teacher or PTA member or in anyway linked to the school and have two children. One is hard working, determined, committed, turned up to every practise, always learnt her lines/practised her music/did any prep work required, was well behaved, always volunteered. She got picked for things all the time, she also put effort into doing the best job she could do. My other child, whilst perfectly capable is inclined to be lazy, puts in little effort, is scatty and will miss practises (or prioritise a more fun activity), will leave things like learning lines til the last minute, can be prone to mucking about - he often (but not always) volunteered, but would be picked far less often that my other child. Rightly so, simply not as committed.
If your child really wants to be picked, then they have to make sure that they consistently show the behaviours that make them the best child for the job.
This continues in Secondary BTW, and is even more pronounced. Prizes at prize giving will go to either the best or the one who has consistently made the most effort. Sports teams are picked by the best player. Choir/orchestra are usually filled on talent. Form captain/sports captain/house captain/Head boy/girl are picked based on how a child behaves. There's no more "everyone gets a turn to be Star of the Week". If you don't put the effort in, you won't get the reward.