Expected value is already what most forecasts show. Expected value conveys information poorly in some common cases, like thunderstorms in the summer. It is very different to hear there's a 20% chance of a thunderstorm, dropping an inch of rain, vs. a 100% chance of .2" rain - the former needs a backup plan to deal with rain, the latter needs to plan for rain. Hence I prefer the text forecasts from the NWS, which list an amount possible, plus more in thunderstorms, rather than a bare number.

Meanwhile the 'probability' listed in forecasts is also well defined as an expected value - it's (probability of X% rain coverage) * (X %), over all X. (Rain is defined as > .01")