Every shutdown leads to a negotiation of the new budget that invariably entails more "austerity" and cuts to government services. You see it in the most recent proposal to keep the government open and the things they cut. I haven't done deep research on the last 3 government shutdowns to list out what has been privatized each time, but the ratchet of privatization continues to turn and each shutdown creates a big loss and austerity aftermath that paves the way for the next round of privatizaiton.
I don't understand what you are arguing. My original point is that the Dems are not really that opposed to the periodic shutdowns because they, being neoliberals, don't actually care about providing government services or funding anything other than the military and their rich friends/donors. Your original question was
My answer is (again), they don't really care if the reps shut it down or not. Despite what they say when they campaign, they don't actually care about keeping anything other than the military and the carceral/border control systems running. It's not an elaborate 3D chess move. It is the same Janusarian one-party shit they always pull. Pretend like they are fighting the republicans tooth and nail to keep shit going, but when it actually comes down to it, they will happily shed stuff like gender-affirming care for military kids as part of the "bargain" to get the bombs to Ukraine and the Zionist entity.
The shut downs don't hurt them or their donors, only the working class people whose services get interrupted and whose living conditions suffer, which coincidentally also helps their donors.