I wonder why most companies can't operate separate teams with these different flows? The "we need it now" crew having their own team who tries to line up dev with the upcoming, etc? I can understand needing functionality "urgently" - in an agile manner, however that will certainly have more costs short-term and potentially long-term if cutting corners.

Every successful or even sane team I’ve worked on had discipline first and Agile second.

Agile processes still require disciplined management. If you have hurricane leadership, it'll still fuck everything up, and you won't deliver any value.