Not really the best design
Those designs were mainly used in mines and factories where an open fire could cause a massive explosion. They weren't more efficient than standard steam engines. While they did store steam at a superheated temperature and pressure, most of the energy storage came from superheated water under pressure that was also in the "thermos bottle".
The most efficient heat engines derive their power from converting liquid to a gas (e.g., water into steam, or gasoline into gases from an explosive reaction). We've gotten pretty good at doing this as efficiently as possible. The problem with the liquid air design is that you have the added step of converting gas into a liquid first. You'll always have added inefficiencies from that no matter what.
