I’m not really clear myself, I just know from browsing the Maple documentation, that they rely on integer (or rational) coefficients, presumably because it simplifies something. Page 2 of https://arxiv.org/pdf/1605.00410.pdf seems to suggest that one of the problems is being able to guarantee that it’s possible to determine the sign of a polynomial near its roots. It also seems (page 8, paragraph 2), that there might be some implications to a heuristic that switches between MPFI and exact arithmetic depending on which is expected to be cheaper for a given subproblem.
Another guarantee from integer coefficients is that it’s possible to pre-filter and ensure no rational roots, so we don’t have to worry about corner cases where a root falls exactly at an end-point of an interval.