While I don't think it would prevent our troops from having foreign-produced trucks in theater, we can't affordably procure such trucks thanks to the Chicken Tax. I would also guess that giving a DoD contract to Toyota for a truck that may not be registrable in the US would also face institutional resistance.
Toyota has factories in the US where they produce pickups. They could build the Hilux here if they thought it would do well in the market.
Also, because of CAFE standards, the US can't even attempt to create its own competing light trucks as everything needs to be fucking massive to maintain the emission exemptions.
The thinking was it would make cars more efficient but instead everyone just built obscenely large vehicles that were classified as trucks instead of passenger vehicles.
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The military has an incentive to ensure there are plenty of Americans who know how to design and manufacture things. A truck and a tank have a lot in common - if war breaks out we want the ability to take people of of trucks and get them making things the military needs.
This is the same reason the Navy has for building ships in the US even though they can be done other places cheaper.