Most folks do not support State womb control before that stage of gestation where personhood has developed, and few believe in the extremist "instant baby" notion where conception produces a person instantaneously.
People can believe whatever they choose to believe, but to evoke the coercive power of the State to impose their personal (usually religious) coercion upon others is antithetical to what the majority of Americans want.
The extremists’ view and their desire to impose it upon others via state coersion is not the moral position of most Americans. If and when a fœtus achieves a stage of development where it is sentient and viable, it is recognized as a person and entitled to legal protection. Before that stage, a person does not yet exist. and the State must respect the prerogatives of the individual upon whom the developing entity is dependent, hence, Roe vs. Wade
Roe v. Wade has nothing to say about "life" nor the definitive timetable under which 'viability' occurs. It's arguing the circumstances under which the state can claim to possess a compelling interest which over-rides the privacy rights of the mother- nothing more. It neither requires them enforce or concede those interests, nor does it limit the circumstances in which a state may have an interest to just those. It merely presents a set of limitations relevant to the statute at hand- strict prohibition of abortion under any circumstances. It is providing one argument why that one law was unconstitutional.
The section regarding the second trimester dictates the point in which the state's interest in the mother's health can override her unrestrained privacy rights. Essentially, it represents the point at which the state can regulate certain aspects of abortion to protect the mother from herself.
The viability issue is completely separate- it represents the point at which the state's interest in protecting fetus's rights can be argued to override the mother's. Although the third trimester is generally held up as the benchmark for this, it was a compromise- the medical definition of viability clearly out-weighs any artificial timeline, and, given sufficiently advanced medical technology, can clearly kick in before the state's interest in the mother- i.e. if it became medically routine for a fetus to live outside the womb at the age of two weeks, that would be the new test for when the state could, but not necessarily must, impose its interests in protecting the fetus over the privacy rights of the mother. The viability issue would then render the interests in the mother’s health moot, if the state chooses to peruse it.
