When the HSA gets to zero you reach your yearly max and insurance takes over and you don't pay any more.
I'm not sure how Amazon works, but my plans works something like (I'm rounding to make it easy, the reality is slightly more complex) that I pay everything for the first $3000, then for the next $15,000 I pay 20%, and thereafter I pay nothing. My total out of pocket is $6000/year, which is also the most I can put into the HSA per year, and my employer matches some of my contributions to in reality I'm getting $7k/year while only a few rare loop holes can get me close to needing that much. It is very rare for anyone to have more than $18k in medical expense per year (I had a baby last year and still am well below that), so for most people the HSA is another retirement account.
Now the HSA does mean I'm not paying $100/month for my insurance, but instead $600/month. However most of the money is invested using the HSA as a retirement account for my medical needs. The idea of the HSA (which has not worked out in practice) is because the money is mine I'll have incentive to shop around for cheaper medical procedures to make sure there is more money for my future retirement, and this should lower costs (in practice most medical things can't be shopped around for, but a few people do look at their itemized bills and sometimes notice a billed procedure that wasn't done).
Now that $600 is $3-4/hr, which is not insignificant to someone making $15/hr. However here again things get complex. That money is pre-tax income, so your taxes are almost cut in half for the year (granted this is only $500 - and only for a single person who can't claim anything else).