Can you really say they are worth it?
Yeah, I agree that I'd be annoyed with standup at any time before 11:30, but 11:45 is perfect and basically doesn't interfere with anything. In a certain sense it doesn't cost any dev time at all if you take it for granted that your developers should stop coding midway through the day and eat lunch. (We absolutely do not eat lunch during standup - we have standup, then we physically leave the office to go eat.) Sure, some days we end up in endless meetings which mean we're stuck in the building eating takeout, but that has nothing to do with standup.
PS: You do lose a little time gathering, and people generally spend some time organizing there thoughts etc. But, keeping track of a short synopsis is useful, as is knowing what other people are working on, and most importantly when someone get's stuck working on the same things for a few days. It also adds a lot of pressure to get at least one thing done every day, which many people slack on.
You might want to speak to your manager next time something like that is happening, because there's no way it can be good for your productivity or the other people on your team. It's certainly not a normal practice. At the very worst, if someone isn't pulling their weight they should be dealt with in private.