The issue with that idea is that the qualifications for President and VP are identical according to the Constitution. So if she is in the office of VP now, it is implied that she is eligible to be President.
The Constitution only addresses the requirements for President.
Kamala Harris is a natural-born US citizen, as indicated that she was born in the State of California and was sworn in as Vice President without objection on Jamuary 20, 2021.
There is ZERO chance that any Court will overturn the Obama precedent (British subject at birth), and I would be astonished if any US court would even hear such a case.