Make every element of an array displaystyle?

You could insert \displaystyle into the column definition, such as

\begin{array}{*3{>{\displaystyle}c}p{5cm}}

Here I used syntax provided by the array package:

• >{...} can insert commands before the array element
• *n{...} repeats a column definition n times

So in the example we get 3 columns, where all cells have \displaystyle, and 1 paragraph column without.

You can use \everymath inside a scope:

{ \everymath={\displaystyle}
  Inside:

  \(
     \begin{array}{cc}
       \frac12 & \frac12
     \end{array}
  \)
}

\medskip
Outside:

\(\frac12\)