You're right that legal expertise is essential to drafting bills. But you don't need to be a lawyer--you can also hire one. Legislators have lots of expert resources available to help with drafting including the offices of legislative counsel[1] and professional staffers and committee aides.
Which is why I compared the elected official to a product manager rather than the programmer. Product owners don't have to be technical, but the best ones often are. And in the cases where a non-technical PM is the best, they're usually bringing some other form of expertise to the table.
I think scientists writing laws, assisted by the legal expertise you mentioned, would be a positive change. They have that other form of expertise. But I also take issue with the above implication that lawyers are somehow unfit to be politicians. They are, in my analogy, the technical product managers. Absent some other form of expertise, having a lawyer in that position is probably the next-best option.
[1] Example from the House of Representatives: https://legcounsel.house.gov/HOLC/Before_Drafting/Ghost_Writ...