Blocking out, say, 2x2 hours each day for "problem management" (fixing root causes of recurrent issues) becomes easy in that situation, with no subterfuge needed. Alternatively, you can nominate part of the team to be either on-call or entirely dedicated to incidents, shielding everyone else who can be dedicated to strategic work full-time (obviously, you need to do regular rotations).
The team themselves often need help in adjusting to that (firefighting can make you feel like a hero so, although stressful, it can be addictive). Blocking out specific timeslots can be helpful from this point of view, too - incidents often seem a lot more manageable if they're not crashing in on top of you at unpredictable intervals.
Then the heroic engineers get promoted and then learn that they can use their weight to shove others around. Meanwhile the ICs that had to do fire drills to make crap happen don't typically get anything out of it, other than watching some manager that shoved them around get promoted.
:/
To me this seems like a matter of company culture that is set from the top. If CTO and VP level act like that, it trickles down and that tone becomes the norm. In either way.
(Am open to better approaches though! Not saying I particularly enjoy last minute urgent meetings you can’t say no to. But most often those are important and with people whose agendas need more care than mine.)
We had a publicly viewable calendar policy. And I couldn't believe the audacity of people in other areas to take it upon themselves to just book over the top of existing meetings because they had decided their meeting was more important. And I'm not talking a group meeting where it's hard to find a gap that works for everyone, these were essentially 1:1 meetings where the organizer was someone with a little more seniority. No polite ask/DM first if it's ok, or a note in the invite to explain. Just see "focus time - no meetings" or something else _they_ deemed not important and they'd schedule it in that block and assume the IC wouldn't challenge their authority.
So had to play them at their own game to give my team their time back. The meeting was as much as an invite to them to challenge my authority as their previous attempts were. Conveniently it worked and nobody would book over my meeting. I do not miss working for larger companies.