There are some.
Low Vf schottkys have the following issues:
* Quite limited reverse voltage ranges,
* Significantly higher leakage current than standard PN diodes,
* Leakage current which shoots exponentially through the roof with increasing die temperature, easily causing thermal runaway.
* Leakage current also increases with increasing reverse voltage, although not as aggressively as with temperature.
There are some very low-Vf schottky diodes available, but the lower the Vf, the higher the leakage current usually is, so you need to be careful in design. Unlike with normal diodes, you can't assume reverse power dissipation to zero; you actually have to calculate it in worst-case conditions, and even if it does not lead to thermal runaway and self-destruction, it could offset the benefit to zero.