Yes, teas should always be shaken. First, they're marketed as shaken iced tea, and we should give the customer the product we're advertising. Second, we store our tea base at room temp. Shaking it with ice is what chills it. Third, not shaking it does impact the taste, especially if it's a tea with an infusion or a syrup or a sugar, maybe not a lot but I'm a tea drinker and I can always tell.

Also most people who aren't shaking are just pouring directly into the cup and not using the shaker for measurements so your ratios are going to be off... Trust me even the most seasoned barista isn't eyeballing it perfectly. That's why we have shakers! And honestly this is like a couple of seconds. Not shaking beverages is not the thing killing your drive times...

I get it, they're putting you under pressure but not making drinks to standard shouldn't be the solution.

The fastest drive thrus I've worked in really perfected beverage sequencing so that's what I recommend brushing up on. There's job aids on the iPad under store support.