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Why do employer contributions count against HSA limits? 
Just like all employee benefits there is a focus on removing or limiting owners of businesses' ability to abuse tax preferences under the guise of an employee benefit. As you point out there is an overall plan maximum 401(k) for employer contributions and match contributions.  There is a nondiscrimination test for FSA programs (there is also a nondiscrimination test for medical plans under sections 125 and 105(h)).  Employer contributions are counted toward the total of HSA contributions.   Why an HSA has a different maximum arrangement than 401(k) is anyone's guess.  But the purpose of the limit is to prevent owners of companies from setting up plans that do little more than funnel tax free funds to themselves.  An owner/employee could pay themselves a wage, contribute the maximum, then have the "employer" also match the maximum, so there are limits in place.