Depends
It depends on all sorts of things. Yes, some airlines "discriminate" in terms of which fare levels get to choose which seats and when. But, if you have an airline that doesn't discriminate it may have some rules that it tries to apply when it is allocating seats (like keeping families together and putting babies by bassinette positions and there can be quite a lot of such rules). On a full flight that can mean there are very few open positions at check in. I've even been faced with a situation where I was told - this is your seat, you can't change it.
As for the percentage of no shows it varies enormously. If all (unlikely but no impossible) the passengers are travelling on tickets that can be changed and refunded with no penalty the rate then the no show rate could be very high. There are all sorts of variables; business vs tourist passenger types (not fares), days of the week, time of day, fare paid.