Modes are very useful when you want to find a complimenting scale with an altered chord. For example you can play a regular C Major scale ( C D E F G A B) with a CM13 chord (C E G B D F A). However, this Major scale will clash with the chord if the chord is altered; For example C13 or CM13b7 ( C E G Bb D F A). It would be useful to incorporate another scale such as the C mixolodian.((F major scale)C D E F G A Bb) This scale contains the b7 or dominate 7 that is need to accompany the C13 chord.
A chord that contains all major intervals will usually go with any mode with respect to the original key.(i.e second degree scale of C, D minor, will go with C ionian, D Dorian, E phrygian, etc) because they all contain the notes of the C major scale.
Modes are not limited to the major scale. They can be used with any scale. For example,the chord C7b9b13( BbDbEAb)could be used with a C mixolodian harmonic minor scale
( F harmonic minor scale - C Db E F G Ab Bb)