History note: When TSP began, the Military did not have the option of contributing. It wasn't until the mid 1990's that talk of adding the military even began.
At the time, (Post Gulf-War, big post-cold war draw down) there was a lot of opposition within the military to the TSP. The thought was, including at the senior levels, that offering the TSP was going to be the pre-thing to doing a massive change in the military retirement system. Rumors circulated that if they gave the Military the TSP and matching, that the federal government would then change the retirement system and do away with the 20-and-out retirement.
That in at of itself killed Congress's adopting TSP for the military for several years. It wasn't until around 2000 or 2001 that Senior leaders in the military finally relented, and agreed to allow the TSP to be offered at all. And then it took a little while to get Congress to approve it, and when Congress looked at it - they said they would let people DO the TSP in the military, but if the Military wanted any matching funds, they would have to do that out of existing budget dollars, and ...well, that's how we got to where we are today.
The good news is that active, Guard and Reserve people can all now establish a TSP account.
The bad news is that the Guard and Reserve do a horrible job of publicizing it, and even the active forces have a long way to go to get participation rates up. especially with no matching funds. .