So the issue is to what extent a state can place an arbitrary burden on a Constitutional right.
Folks here will predictably howl when the SCOTUS finds that such arbitrary burden is un-Constitutional. But if the SCOTUS were to apply similar thinking to the gun right, folks here would predictably applaud.
So its just the same old story - both right and left support "rights for me but not for thee".
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed
Life was mentioned first, because without it all else is moot. That primacy is for a reason.
When the rights of one overturn the rights of another, we truly have "Rights for me, but not for thee", as you state, but when the lives of the mother and child (even still in the womb) are held equally sacrosanct, then there is equality.
The mother's situation is temporary, limited by natural gestation. Motherhood need not follow; there are plenty willing to love and raise a child. The remedy you propose, while more immediate in its result for the mother, has permanent and detrimental results for the baby. This is a disparity in effect that should not be allowed,the permanent removal of the unalienable rights of the one for the temporary inconvenience of the other is not a balance any jurist should condone.