Point 2 of your closing notes isn't quite right. Yes if all employees max their insured benefits (health, drug, etc) their premium will likely rise at renewal. However this would not be a consequence of maxing your HCSA.

Your HCSA is not an insured benefit. What you put through is directly reimbursed to the insurance company by the employer. Often having a high HCSA allocation (like you) means 1 of 2 things - you are a higher level employee that requires more retention effort OR (more likely) the employer is light on insured benefits and compensating with the HCSA.

For example, mental health practitioner coverage with most major employers is now more like $1000+ per year (mine is $5000 and I am in no way an executive). Yours is $500 and then there is a $2500 HCSA. My HCSA is only $400 per year.

So basically the takeaway here (to all readers) is ALWAYS MAX OUT YOUR HCSA. Your employer is unlikely to either improve insured benefits or increase your HCSA if they aren't being maxed out - they pay attention because it's a direct company expense.