I've already answered your question: I don't believe that.
So the final decision making power would rest with the doctor then, and not the woman. So much for "any reason, any time" and "trust women".
If you support the removal of any legal time limits and for the final decision making power to lie with the doctor, would you retain any reference to 24 weeks in the legislation at all?
Because at the moment, a woman seeking an abortion for non medical reasons prior to 24 weeks needs sign off from two doctors. In reality this is a formality, in the same way that the King giving Royal Assent to a piece of legislation or inviting the person who has won a general election to form a government is a formality. Doctors who suspect that having a termination may not be in the woman's best interests, for example if they suspect that she is being coerced, may ask more probing questions and do more safeguarding but they will not ultimately refuse as long as she is within the time limit.
If you remove any reference to 24 weeks, how will women know when they must act if they want to have a termination for non medical reasons? What if her doctor would sign off on it at 22 weeks without really questioning her decision but at 30 weeks would say, "No, I don't think this is in your best interests"?
How does this new, more flexible legislation help her?
What if a pregnant 14 year old who has been raped by a family member would be granted an abortion at 30 weeks by one doctor, but not by another? You have created a completely opaque postcode lottery where a woman under the care of a particular hospital will be treated by a doctor who will agree to a termination in her particular circumstances, but the same woman under the care of a different hospital would be refused one.
How is that fair?
What if there are currently thousands of doctors up and down the country who privately disagree with carrying out abortions past 20 weeks, or even past 15 or 16 weeks, but will do it because they understand that their approval is a mere formality and knew this when they agreed to take the job? If you remove the reference to 24 weeks in the legislation and put the decision making power in the hands of doctors instead, not only have you created legal uncertainty and an effective postcode lottery, as explained above, but you have also put the access that women currently have to abortions before 24 weeks at risk. Because there is no longer a clear cut off point, before which doctors will agree to perform abortions without asking too many questions or saying it's not in the woman's best interests, and after which their hands are tied by the legislation.
Isn't that quite risky?
It's all very well to have these cool sounding principles such as "any reason, any time" and "trust women" (as if anyone should trust a woman who is in labour and high on meths saying she wants an abortion, or a visibly terrified woman from a certain culture who is pregnant with a baby girl and accompanied by a man who is almost certainly abusing her), but when you actually test these theories with hard cases, they fall apart.
The job of lawmakers is to anticipate these unlikely but tragic and difficult scenarios and assess whether the proposed law actually produces the best outcome. If don't test the new law against every possible scenario you can think of, or if you pass it due to political pressure in the full knowledge that it could cause bad outcomes in certain scenarios, you have made bad law.