I think your observations are very astute. It does depend a lot on where you live. But you aren't telling the whole story. The military does not live on their basic military pay alone.
The biggest factor you omitted was the "basic allowance for housing" or BAH. If your Staff Sergeant was living in Chicago zip code 60007, he/she would be drawing $1929 per month as BAH (with dependents) or only $1608 (without dependents). However, the BAH would only be $1110 for Bentonville, AR or $855 without dependents. Thus it does depend greatly on where you live, but regardless, it's still very significant when you stack it up against the base pay you cited. There is also the "basic allowance for subsistence" (BAH) which is an additional $369 per month. Then there's the fact that both BAH and BAS are completely tax-exempt. People don't realize this but these two nontaxable items can make the difference between poverty and doing pretty well.
Then there are other factors, such as the fact your Staff Sergeant today would be getting these benefits without the need for a college degree. He or she will, however, get the full GI benefit which will ultimately pay most of the cost for said college degree. He or she will also enjoy completely free medical and dental care for himself/herself and his/her family. He or she will be able to retire with a very nice lifetime pension after 20 years of active duty. If said Staff Sergeant had enlisted at 18, he/she would be retired and drawing a lifetime pension at the ripe old age of 38, also with lifetime medical benefits. How many civilians get a deal like that?
Our military earns its pay. But let's not pretend the military is suffering financially. The ones who suffer the most financially are those in combat zones. Incredible as it sounds, the "imminent danger pay" is only $225 a month for serving in combat zones. We give everybody in the military an annual pay raise, including the guy who's a pay clerk working garrison duty M-F 7:30-4:30 at Fort Leonard Wood, but we give the guys risking their necks a measly $225 a month? That's criminal.