Even in Germany my (private) deductible is 3000 EUR so if I thought I might need "something done" I'd try to do it early in the year: if I spend 2999 in December the counter resets on January 1st. And I'm told I have a pretty sweet deal compared to America.
Also, I’m not sure if the out of pocket savings make up for the compounded investment earnings of a triple tax advantaged HSA contribution. However, it could work if both spouses get insurance from employer and they already have a kid, and the husband chooses an HDHP with HSA and puts one child under his insurance so he gets to contribute max amount to HSA, while wife chooses low deductible low out of pocket max plan and puts new baby under that.
But I wouldn’t waste my time figuring that out or doing that paperwork, it can’t be worth the different in out of pocket maximums and deductibles if you account for the headache of doing the paperwork.
As an Australian medical student I'm horrified to think that this would be a genuine "hint" that would be relevant in a first-world country.