As always the Democrats presume that the electorate is stupid. And as is usual, they are probably right.
First, there will be no Democrat majority in the House come January, and Biden knows it. Second, the President does not introduce legislation. Third, Roe v Wade was dead long ago - superseded by Planned Parenthood v Casey. Fourth, the USSC recently ruled that the Feds have no power to regulate abortion under the Constitution.
Whew!
Fifth and most important, today's LEFT would never accept the "Roe v Wade" formulation. Under Roe, the "right" to an abortion only exists in the first trimester. After the first trimester, the States have power to regulate (or prohibit) abortions, and during the third trimester abortion is only acceptable if carrying a baby to term seriously impacts the "health" of the mother.
So would Biden seriously try to codify RvW? NFW.
Either (a) he is an idiot, or (b) he thinks we are all idiots.
Or both, I suppose.