I suppose I should have qualified that with "don't pay much income tax?"

Depending on your rank and what your active duty is like, much can be excluded.[1]

> Combat pay: Compensation for active service while in a combat zone

Combat zones: much of the middle east, including relatively stable countries that aren't Afghanistan or Iraq, as well as the Balkans.[2]

> Enlisted member, warrant officer, or commissioned warrant officer. If you are an enlisted member, warrant officer, or commissioned warrant officer, none of your combat pay is included in your income for tax purposes.

For officers, the exclusion has a threshold. That threshold is:

> For 2019, the applicable amount is $8,803.50 per month

Or $105,600/yr income not subject to taxes.

In addition to BAH being excluded as you mentioned, there's also BAS, BAS, OHA, other housing benefits, moving and travel, healthcare, all not subject to income taxes.

These are all sources of income (in an accounting, not IRS sense) civilians would need to pay taxes on. As a result, active military pay a much lower tax rate on their income than civilians with the same pre-tax income.

[1]: https://www.irs.gov/publications/p3#en_US_2018_publink100017...

[2]: https://www.irs.gov/newsroom/combat-zones

Majority of people are in a combat zone for about 6mo at a time, and not a lot of them ever end up going at all. I never was selected for any tax exempt duty in my 8 years as an enlisted member of the USAF, and anecdotally know a lot of people who over a 4-6 year (usual single enlistment length) career who either only were deployed once or never at all.