The Chinese government is leading (and funding) massive efforts in high performance computing and AI. If they win, entire high tech industries could be situated in (and lead by) China.
It actually works out better if the US government computers are through various science organization labs, because it locates much of their computing power in places also accessible to universities and at agencies amenable to US universities using their resources. So funding computers through the DoE, NOAA, NASA, etc actually makes them more available for the US research community, while allowing the military to lease the time they need (eg, for calculating explosion dynamics).
The total funding for US supercomputers also could be higher, but that's a general problem with US infrastructure investment.
My main point was there's no real concern with the computers being owned by scientific institutions instead of the military -- they're still government funded, it just makes them more widely accessible for use.
I seem to recall that the DoE, NOAA, and NASA always had a lot of computing resources, and that they generally rented time on those clusters out to other government agencies.
I do wish the government would step up on AI though -- I think that they owe it to the country to put together a Manhattan Project for AI.