Gregorian chant is the music which grew to be part of the Mass and hymns (old or modern) are not.

The people sung hymns at old-time Low Mass (on Sunday when the clergy were supposed to be offering High Mass for the people...) but these weren't part of the liturgy any more than little old ladies praying the rosary instead of actual participation (participatio actuosa) was part of the liturgy.  Aside from the Gloria and the Sanctus, hymns aren't really part of either the EF or the OF.  (Of course, they are part of the Liturgy of the Hours, and if the Mass includes a procession a hymn, e.g. Crux fidelis, is typically part of the Mass.)

This is as true of the OF as it is of the EF--that's why hymn singing is a distraction in the OF not unlike a commercial break.

In the past 10 years we've seen some organic development of vernacular plainchant using the Mass texts.  Maybe some day it will be allowed at the EF, as "mutual enrichment".