Usually standup meetings are scheduled at a given time in the day (usually, it's the very first thing in the morning). You know when it's coming; it's not like people randomly poking at you and making you do a context switch.
The productivity is still lost. I can try to get something done before being interrupted by the scheduled time, or I can accept that nothing will get done beforehand and wait idly until he clock finally smiles upon me. The end result is the same either way. Try to fight back against reality as hard as you might, but there are only so many hours in the day and that is beyond your control. As engineers, we should recognize that we have to work in the confines of what we can control.
Fine, catch me the moment I wake up. But good luck finding two team members who wake up at the exact same time each day. That never happens in the real world. No matter how you slice it, productivity is going to be destroyed.
I moved my team's standup to just before most people take there lunch. Initially it was an accomodation for someone who was temporarily working in a different time zone but after they returned home no one on the team wanted to change it.
I like it for two reasons, I go for lunch straight after so don't have two context switches. And it sometimes works as an effective midday target for me to try to get a ticket progressed before the standup.
In practice, lunch does not bring a context switch as you just don't go to lunch until you reach a natural stopping point. Standups cause a context switch because they are scheduled by the clock, not by the work.
Asynchronous standups avoid that problem, but I've never seen an async standup bring any engagement and ends up being nothing more than "I'm working on X again. Duh." which is completely pointless.
Maybe for you, lots of us go for lunch with colleagues, play sports or boardgames and so that tends to happen on a schedule. At least we did until we all started working from home.
Like another commenter said, you can always say "Hey guys, give me 15 minutes while I wrap this up" and you don't enter context switch mode. Unless you work with completely unreasonable people, they'll wait.
In fairness, as you are forcing a context switch for a standup, it is likely that you do work with unreasonable people.
