HSA's (Health Savings Accounts) DO rollover. FSA (Flexible Savings Account) usually DO NOT. Since we are able to roll it over, I think we put about $5000 in ours. Now having said that, we are like you, rarely sick and $2200 sounds like plenty, but you just never know.
Your kids are young, so you don't know about an accident or unexpected illness. Our soon to be 16 year old old needed glasses. But because she is a softball pitcher we also got her specialized contact lenses in addition to her glasses. It was nice to have the extra $ available.
Our son, then 19, woke us up in the middle of the night in horrible pain. Because DH and relatives on BOTH sides of the family have histories of kidney stones we took him to the ER. Unexpected visit that ate about $1000 out of the HSA
I am thrilled with the opportunity to have an HSA! Again, like you, we are over all healthy. But it also makes me look and think harder about prevention and the utilization of our resources.
edited: My understanding of HSA's (or at least ours) it is to cover those otherwise out of pocket costs up to a certain point. Once your hit that deductible (just like any other insurance but higher with HSA) your insurances covers at a higher rate. Of course it all depends on your policy and how the policy was written and brokered to your employer.
I know it sounds cliche, but things are different now. When I first started my nursing career, I had fabulous insurance. AND since I was an employee when I had my kids (16 and 20 years ago) they covered extra so my 'out of pocket' was just 5% Then when I left the hospital and worked in a lung specialists office, I had the same insurance they had for their families which was amazing. When I quit working and went to my husband's insurance, he was an executive with an international company. Again, fabulous coverage. BUT, when he got sick of corporate BS and moved to a smaller company, it was about the same time I started looking at health and wellness differently. It also opened my eyes to the games (just for a lack of a better word, no offense meant) that is played between insurance and hospitals and doctors. When I went in for my physical and explained to my doctor that I now had an HSA she treated me as a "private pay" and it completely changed the billing. ONE test she would have billed $200 to my insurance company because of the deductible and discount process. But to charge me it was $25!
Insurance is there for a reason, major illness or catastrophe. But since I am now kind of an out of the box thinker (chiropractor now before MD) I like my out of the box option.