Are they 1% as inspiring as what the DoD does with their budget? I don't mean to be snarky, but level of inspiration is pretty subjective and difficult to put a price tag on. Honestly, I feel like the NASA budget needs to be considered in context relative to the DoD budget and then these cuts look much less convincing as being necessary.
People aren't inspired by safe shipping lanes. But quite a few are alive because of what global shipping enables.
Captain Phillips was a pretty good movie.
It would be closer to 2%, but we could measure it by engagement. Ask people what their last positive interaction was with NASA vs the military. The military does all sorts of outreach with things like the Blue Angels, stadium flyovers, competitions at fairs, etc. Ask them what NASA has done over the past year vs what the military has done over the past year. Chances are many people couldn't name something NASA achieved in the past year. Would it be at the 2% number? I don't know.
I'm not saying one is better than the other. I think both should look for budget inefficiency, but until those are identified I wouldn't propose budget cuts. But it does seem that the NASA missions could be more inspiring recently.
US Military FY 2024 enacted budget: ≈ $842 billion
VS
NASA FY 2024 enacted budget: ≈ $24.9 billion
That is a ~35x multiplier. By bog-standard logical implication your question answers itself.
I dare say a great many people are very inspired by what the DoD does with their budget. Inspired to what... well, that's another subject. And the most inspired people are not the ones living in the US.