The biggest issue is you now need programmers who know about epsilon computation and error propagation when working with incorrect numbers. Then you need to know when to fudge the visual representation of your incorrect number (and you probably also need to understand when your programming language / libraries do fudge the output for you).

FP numbers have their use but they re better reserved for scientists doing actually scientific stuff and not just to represent what are actually tiny numbers (in the grand scheme of things) and which can be represented perfectly by other means.