Delicate is synonymous with "fragile". Delicate lace collars are fine when in appropriate context, but that context is fairly narrow (when you know it will be protected enough to survive).

As for people, I don't think our culture values fragility in an individual. Conversely, we definitely do value resilience. I'm not sure of a case where you could refer to a physical or mental aspect of someone as delicate or fragile (when it's relative to the norm where it's not) and it comes out positive.

Most people who read that phrase see "delicate" = fragile. Sensibilities are not like a lace collar.