If your deck heavily relies on using the field spell, you can essentially bring more than 3 copies of it by using Zeradias. It helps search for the field spell, but it will be destroyed if it's removed. Divine Punishment is a strong trap card that can only be used when the field spell is face-up on the field. It can negate most things, preventing your opponent from making their key plays.
Meltiel and Neo-Parshath are monsters that take advantage of the field spell. Meltiel lets you destroy any 1 card your opponent controls whenever a counter trap card is activated, while Neo-Parshath uses the field spell to increase its attack and defense if your LP is higher than your opponent, allowing for a potential OTK.
Since Cloudian monsters can't be destroyed by battle, using them together with the field spell means that you can effectively stall the duel, mostly useful if you are farming certain duelists that can't destroy your monsters through card effects. Build up Fog Counters using the other cloudian monsters, and end the duel with a high attack nimbusman to end the duel.