No. it wouldn't. A constitutional amendment is a possible solution but not necessary.
They decided that there is no existing constitutional right to abortion. Thus Federal or State law can regulate or ban abortion.
Likely it will be decided state by state. But a Federal law would also be a possibility. A Federal law is possible to ban abortions, regulate abortions, or allow abortions. Depending on that hypothetical law states might be able to or not able to restrict abortions. Biden, and now Harris, want a Federal law that forbids any state restrictions on abortion. Trump seems to want no Federal laws that would interfere with states deciding for themselves.
Nope. A Federal law, presuming it would likely pass constitutional muster, would be an adequate way of having a consistent nation-wide policy. One way or the other. We had a patchwork policy on slavery, with some states saying some human beings were not persons while others said they were. That compromise did not endure. One that denies personhood to persons based on location can't survive.
That's mostly because Trump decided he wanted states to decide and not the Federal government. That's his preference. It's not how it has to be. With a Trump presidency and Republican majority the states decide. With a Harris presidency and Democratic majority there will be a Federal law allowing all abortions and that restricts any states from deciding otherwise.
Some Republicans are happy with that. Trump is happy with that so he probably gets his way if he is elected. Democrats will not allow states to decide. They don't want any restrictions on abortion and will push for a Federal law ending all abortion restrictions, packing the Supreme Court with people who will overturn the overturning of Roe, and a constitutional amendment in favor of abortion.