Even if you believe that the ordering the National Guard to DC is going to address homelessness in some positive way, Trump doesn’t care about that. Mobilizing troops to DC is the latest step in his efforts to dismantle democratic government and consolidate power.
Cleaning up DC is item #11 on Trump’s 2024 platform: https://www.donaldjtrump.com/platform (“REBUILD OUR CITIES, INCLUDING WASHINGTON DC, MAKING THEM SAFE, CLEAN, AND BEAUTIFUL AGAIN.”).
Your complaint isn’t really about “dismantling democracy,” but instead about Trump running roughshod over all the Democrats who run DC even when the people elect a Republican President, such as the anti-democratic permanent civil service. DC is the people’s city. It is constitutionally a federal enclave, and under the DC Home Rule Act the President has the right to federalize the police. Trump did so to carry out the policies people voted for.
No I mean small-d democratic rights which Trump has been eroding as he consolidates power - retaliating against free speech, deploying federal forces against protestors, suspension of due process, concentration camps, and undermining the independence of the judiciary by attacking judges. By limiting our focus to the legal justification of the militarizing of DC we miss the big picture - erosion of small-d democratic norms and processes in our country.