People can think about all sorts of random stuff while they're doing their morning workout, taking a coffee break, enjoying lunch, or whatever. Obviously you're right that that sort of thing is costless.
On the other hand, somebody actually had to take time out of their day to prepare the general's remarks, run through them, and set up this little viral moment during the general's work day. In hindsight, that time obviously could have been better spent on stuff related to running the military.
When organizations get woke, it isn't just people thinking about stuff in their spare time. Wokeness becomes part of the institutional mission, which means it gets resources -- specifically time, money, and mental bandwith. Those aren't infinite resources. They come at the direct expense of the job the institution was supposed to be doing in the first place.