I would respectfully disagree with the notion that “internalized shoulds” as you put them are universally undesirable. I think there is a distinction to be made regarding whether one voluntarily internalizes a new set of values, versus whether those values are forcibly imposed from outside.
For example, I am currently taking up an exercise regimen. One of the ways I motivate myself is by telling myself that I want to be healthy, so I should go exercise. This is opposed to telling myself I should do something because someone else told me to do it.
Another example is that my friend wanted to get good at art. But he was inexperienced, so everything he drew at first sucked. But he kept telling himself that in order to become good he “should” draw every day. In the initial stages, before his art improved to the point that it became its own reward, that internalized should was the only thing keeping him going.
I think that “internalized shoulds” are a stage that every new habit that you’re trying to build goes through before it becomes an internal motivation. We shouldn’t prematurely cease building habits because we feel that resistance in our own minds.