Breaking things is time expensive too, plus it erodes trust.

Not breaking things can be time expensive if you do it late, but it doesn't have to if you do it early. If making sure you don't break something is time expensive then you're probably not building on a solid foundation and solid processes.

Be foundation first. Incurring the time expensive to build a foundation (process, infrastructure, software) that will allow you to move fast with stability IS controversial; because it's not the "hack" approach.