Roe V. Wade set several precedents. One of these legal precedents was to uphold the right to individual bodily autonomy in medical decisions based on an interpretation that the constitutional right to privacy extended to medical decisions. (obviously "bodily autonomy" doesn't apply if you consider the fetus to be a separate life. But that was not the court's take)
Back to the main point: They cannot mandate the vaccine if you have a right to privacy and bodily autonomy in medical decisions.
And even without a federal law like Roe, blue states would still keep abortion legal.
So I suspect the federal government is willing to sacrifice Roe V. Wade if it means they can mandate the vaccine.
Thoughts?
What the hell makes you think the government is worried about "too many fights". Events like Waco, ruby ridge, and 6 months of BLM terrorism in 2020 should prove this is not a worry of the Swamp lmao. They need to erase bodily autonomy both from being a cultural value, and from law as much as possible.