The Sacred Congregation of Rites, in its Instruction of 3 September 1958, decreed:
13. a) Latin is the language of liturgical ceremonies... Any
exceptions to the general rule of Latin will be mentioned later in this
Instruction.
14. a) In sung Masses only Latin is to be used. This applies not only to the
celebrant, and his ministers, but also to the choir or congregation.
"However, popular vernacular hymns may be sung at the solemn Eucharistic
Sacrifice (sung Masses), after the liturgical texts have been sung in Latin, in
those places where such a centenary or immemorial custom has obtained. Local
ordinaries may permit the continuation of this custom 'if they judge that it
cannot prudently be discontinued because of the circumstances of the locality or
the people' (cf. canon 5)" (Musicæ sacræ disciplina: AAS 48 [1956] 16-17).
b) At low Mass the faithful who participate directly in the liturgical
ceremonies with the celebrant by reciting aloud the parts of the Mass which
belong to them must, along with the priest and his server, use Latin
exclusively.
But if, in addition to this direct participation in the liturgy, the faithful
wish to add some prayers or popular hymns, according to local custom, these may
be recited or sung in the vernacular.
So there you have it. No vernacular allowed at High or Sung Mass - the concession to "immemorial custom" in 13a applied to German dioceses who had celebrated 'Deutsches Hochamt' (German High Mass) for ages anyhow. Vernacular hymns at Low Mass were allowed, but nothing else could be sung at a Low Mass, not even the liturgical texts.
And there you have the genesis of the hymn-sandwich. After
Sacrosanctum Concilium, singing of vernacular hymns was encouraged to aid 'active participation', whereas both the translation and the musical setting of Missal texts were reserved to Episcopal Conferences and their commissions. You could sing hymns, but
not the liturgical texts! Two temporary versions of the Ordinary eventually appeared and there were some musical settings of the second one (despite "and peace on earth to men who are God's friends"!), but it was not until the 1st Sunday of Advent 1969 that the new Order of Mass and Missal with the current ICEL translation, JB (and RSV) Lectionary and Grail psalms came into use. By then the hymn-sandwich, assisted by new hymnals, was well established.
Whether the hymn form is actually suited to the processions at which it is used has never been seriously debated in this country. Hymns in both the Roman and Reformed traditions are essentially set pieces sung for their own sake; during them nothing happens: look at the Gloria in excelsis, the Te Deum and, of course hymns in the Divine Office - hymns used processionally at the Palm Sunday procession and Good Friday Veneration are rare exceptions.
The Communion procession is an obvious case where the hymn is an inappropriate textual form. And a recessional hymn is not strictly part of the Roman rite: it is only mentioned once in official documents (1967 Musicam Sacram instruction, para 36) and this I reckon to be an editorial oversight. "Go in peace... but wait for the final hymn!" In Mediterranean countries the congregation take the dismissal more seriously and are out of the church doors before the priest has a chance to get there! Shouldn't we in this country take ritual instructions seriously too? GIRM (88) provides a hymn - yes, a set-piece hymn - after Communion as an alternative properly integrated into the rite.