To be fair, the problem you describe isn't inherent to 80-bit floating point values. If you use 80-bit values in your ABI or language definition, it won't occur

To be fair, the problem you describe isn't inherent to 80-bit floating point values. If you use 80-bit values in your ABI or language definition, it won't occur - it occurs when you try to user a wider type to implement a narrower type, e.g., implementing 64-bit floats (as specified in the ABI or language) with 80-bit operations. In that case, the extra precision is present and "carried across" operation when registers or the dedicated floating point stack is used, but is discarded when values are stored to a narrower 64-bit location. So the problem is one really of mismatch between the language/ABI size and the supported hardware size. Of course, 80 bits isn't a popular floating point size any more in modern languages, so this happens a lot.