I'm not sure that the draft is actually at all indicative of the final decision.
As of when the opinion was drafted (in February), it is likely the majority was intending on overturning
Roe. Obviously, the leaking of the draft opinion (along with what is very likely to be future violence on the part of the left) is intended to intimidate the justices into changing their votes. It is not uncommon for justices to change their mind about a particular vote after reading the opinions of the opposing side.
Legally:
As I understand it, Roe v. Wade was based primarily on the argument that prior to the third trimester, the 14th amendment's right to privacy prohibits any government in the US from interfering with the mother's personal health decision.
I find this argument to be bogus. Healthcare is fairly heavily regulated by the government, and the government has made illegal various procedures, such as those required for organ harvesting/trading, and assisted suicide.
Although I am generally in favor of a free market, I don't believe there is any tangible benefit to society to allowing the
selling of organs.
There are other regulations with regards to healthcare that are a net positive to society (granted, there are some regulations that are a net negative).
I think it is best to allow voters to decide the level of regulation that abortions should be subjected to. If the will of the people is to say that abortions should (or shouldn't) be subjected to particular regulations, I think it is difficult to argue that the contrary should be enforced.
Further, the government (via the will of the people) has outlawed various acts, even when said acts occur in one's home. For example, it is illegal to murder someone in your own home, as well as in your place of business.
Politically:
The Democrats were always going to use this as a campaign tool. Since everything else is going so poorly for them, this is about the only thing they have. I hope you all like this issue, because we're going to be hearing about abortion 24/7 until November.
Democrats will falsely equate
Roe being overturned with abortion being outlawed and will use their various propaganda outlets to repeat this falsehood. They will use this propaganda, to motivate their low/no information voters to vote in higher numbers.