"Will not work" may be putting it a bit strongly. "May be a bad idea" or "needs more thought than you might think" might be a better one.
The current through a diode changes a lot for a small change in voltage. If there is a slight mismatch between the diodes, one can end up carrying much more current than another.
Since the characteristics change with temperature, there is also the possibility that the situation can be unstable - the diode which carries more current gets hotter and its Vf reduces, allowing it to take more of the current, and get even hotter, etc.
Addition of some Ohmic resistance in series with each diode helps balance the currents, by increasing the fwd voltage when the current increases. But of course this reduces efficiency, so may not be appropriate here.
Tying the diodes together thermally, ideally at the chip level, helps prevent thermal feedback exacerbating the imbalance.
This can also apply to putting diodes in series to get higher reverse voltage rating. If their characteristics are not identical, then one carries more of the voltage for each value of leakage current. So you can't assume two 1000 V diodes in series will withstand 2000 V. Maybe one will reach 1000 V while the other is at only 700 V, then any increase over 1700 V will exceed the rating of the first diode.
As CWatters says, it may work if they are well matched. And you avoid thermal problems. And increase your safety margins to cover whatever mismatch there is.