Saver doesn't restrict you to a certain seat; it restricts the seats that you can pre-select. There's a big difference. You can still buy a saver fare if all the seats available for pre-selection are full; in that case you will be assigned a seat (most likely outside the section that saver can pre-select)

People ask GAs for seat changes all the time. Most people do it when they are in a group and did not manage to select seats beside each other. Some people will do it if they are stuck in a middle, and will request to be moved to a window or aisle if one becomes available. I do it when I get a premium seat that I don't like -- I try to figure out if someone in a seat that I want is likely to be upgraded, and I ask the GA if they can move me to that seat when/if they upgrade that person. I just ask politely and I've never been refused. You don't do it at boarding -- I usually try to get to the gate a little early (the GAs usually show up about 1 hr before takeoff) and try to ask them when they are not too busy. They will get to my request when they get to it, and if they don't (or can't) that's fine too. But they are generally very good at their jobs and are able to accommodate people quite well. Of course if the flight is very full you may be SOL, but that doesn't mean that you can't or shouldn't ask (politely, of course).

Just because you're not entitled to something doesn't mean that you can't get it if it's available. Just remember that you're not entitled to it when you ask (ie, you're asking, not demanding, and you need to be ok with it if the answer is "no")