Vodka is arguably superior to other spirits for cooking and infusing for the same reason it makes such a popular cocktail mixer. It can do everything other spirits can do and more. It can blend and enhance other flavours without altering their taste or it can be infused with any number of ingredients to create entirely new flavours.
Exactly how much alcohol remains in a finished food depends on the cooking method and duration. But, as a rule, those cooked at higher temperatures over a longer period will retain less alcohol. In fact, some of the alcohol content of any food will evaporate naturally during preparation or storage - without applying heat. Even the size of the pan can affect alcohol retention since a larger pot will provide more surface area for faster evaporation.