There are different types of massage here; medically trained therapists and those considered to be in the beauty/spa industry. There is some cross-over, but only registered massage therapist costs are covered by insurance.
This isn't government coverage, but private; usually companies with benefits will include a certain amount per year. My company benefits include it with 'paramedical services' including physiotherapy, podiatry, chiropractic, etc. I am lucky to have that benefit, although I don't take advantage of it very often. I have only ever been for 4 massages in the last three years when I have had an issue with my neck or shoulders, but my benefit would cover 10 per year.
I can attest to massage therapy helping with injuries or stiffness and know many would benefit from it if it was available financially.