that perspective is not backed by data, and the administration doesn't appeal everything

very few supreme court cases make it to headline news, and the ones that do are the ones you're thinking about it. those are the ones split by ideological lines, which are less than 10% of what SCOTUS rules on. the government loses many cases unanimously as well. there are some unsigned opinions that do punt things back to lower courts that may be in the government's favor, or not.

all to say, its more nuanced than that. the trend, as a last and compromised bulwark, is there, but that's not how the court consistently behaves.