Technology

The whole point of triaging incoming demands and doing all you can to subtly train the people upstream who are already informed of the importance and urgency of something to only get it to you in a way that interrupts your work if those things are indeed urgent, is exactly to create and maintain the space that lets you address most things in the Non-Urgent Important quadrant before they transit into the Urgent Important one.

If you don't have "thinking things through" and "maintenance/tweaking" time you're going to get a lot more fires and a lot more of the fires which start small grow into full-blown fires before you spot them, all of which just turns into a feedback cycle were all that urgent firefighting means you don't have time for preparation, prevention and detection, which in turn creates more fires and more small fires growing hence you have to spend more time in urgent firefighting.

To be honest, in my entire career I have never managed to, in a specific job, pull out from a "constant urgent firefighting mode" to a "mostly steady mode of work with an urgent fire having to be fought once in a while": making it happen has always been a case of me starting a new job and bringing in best practices from the start, so that by the time I'm finished with learning the environment, and integrating with a new team, and am working full speed, I'm keeping things under control. Doing it from the start of a new job is often possible because in my area (Software Engineering) people aren't expected to hit the ground running at full speed (since you have to learn the installed codebase and integrate with the team) so there's a lot of leway when starting a new job which you can use to set expectations from the start and to justify the extra time it takes to actually get a decent work process in place.

As I've written somewhere else, I've actually managed to bring over and use the Dutch style of working in a British Finance environment (which is hectic and prone to shoot-from-the-hip management and firefighting) to yield better results (faster and more predicable deliveries, were the work I made was better matched to user needs and had fewer bugs) than most of my colleagues and did all this working 8h/day rather than the 10h+/day they did.

IMHO, the process works, and I believe that's the merit of the process rather than being a "me" thing.