Flexibility makes room for individual differences: in needs, in motivations, in life circumstances, in backgrounds.
Consistency makes sure we provide a guaranteed degree of quality, based on the best we know right now from research in teaching and learning.
When you give teachers or students too much flexibility, you end up with a broad spectrum of quality and large gaps in outcomes. These gaps often advantage those who showed up with advantages to begin with.
When you give teachers or students too much consistency, you stifle the inborn drive for significance, creativity, and autonomy. This stifling produces motivational obstacles that many students and teachers are unschooled on overcoming. Heck, in most places, our understanding of motivation is built on anecdotes or buzzwords.*
What we need is quality, consistently-taught curricula: knowledge-rich, multicultural, evidence-informed, vertically sequential, and cumulative. And then we need professional development that equips teachers with the knowledge and skill it takes to deliver such curricula in a manner that honors student difference, cultivates student motivation, and continuously improves the assignments and assessments to hit those sweet spots of optimal challenge for all children.
If this was easy, more countries, states, and schools would be well on the paths to seeing it done. (Some are, but most aren't.) I'm not writing this because it's easy. I'm writing it because it's true and those of us who lead need to think on and work toward these things.
Apart from them, talk about equity is just that: talk.
*There are good models of student motivation that don't rely on buzzwords or massive, programmatic changes to understand and implement. The five key beliefs is one of them. Here are two articles to get you started, here's a one-hour overview PD, and here's an in-depth, fully asynchronous course.