Anyone who thinks standing makes you more alert than sitting has never held a job that requires more than 5 minutes of standing still at once...
Or even looked at someone who has to stand still as part of their job duties.
You may look alert, but a huge chunk of your brain is devoted to how much it sucks to have to be standing.
Like, I've been a part of government security theater and we had to stand. But we just had metal detector wands, the little room with the one way mirrors next to us had half a dozen dudes with AR15s and body armor, they got chairs because they were the ones that had to be ready.
My only job if anything happened was to fall down so I wouldn't be hit when the guys on the other side of the glass opened fire.
We were just the bait/distraction