The reason the compiler doesn't like this is because there's no guarantee Vec<T> won't implement FromStr at some point in the future (you have no control over the standard library), and if that happened you wouldn't know which impl to use.
There's an unstable feature called specialization which tries to relax those rules when it is provable that one blanket implementation is strictly more specific than another, but that wouldn't work here because there's no "stricter than" relation ship between T: FromStr and Vec<T> where T: FromPairs.
Often you can work around these sorts of overlapping impl rules by introducing another level of indirection (i.e. an intermediate trait). Kinda like how we have the FromIterator trait because a direct impl<I, T> From<I> for Vec<T> where I: Iterator<T> would overlap with Vec's other From impls.
To X-Y your question, does your code ever use the FromPairs trait as part of a generic function or are they all concrete uses of the type implementing FromPairs? If the latter, you could be running into the Concrete Abstraction code and would gain a lot of clarity by dropping the FromPairs trait altogether and using normal functions/methods.