As it turns out, the line is a procession. We receive together, as one, so that a certain uniformity of posture is intended.
Having said that, it is also intended that freedom of posture still be allowed those who have individually received Holy Communion. It is not a liturgical abuse to sit or kneel at while everyone else remains standing. It is OK to pray sitting during the sacred silence instead of kneeling, too.
The quote below is taken from adoremus.org/Kneeling-CDW-response03.html:. (Their chosen emphasis was lost in the cut-n-paste; the boldface is mine.)
Cardinal Francis George, of Chicago, chairman of the Bishops’ Committee of the Liturgy, submitted a dubium (question) to the Congregration for Divine Worship and the Discipline of the Sacraments on May 26, 2003, concerning the long-standing practices of individuals kneeling upon returning to their places after having received Holy Communion. Cardinal Francis Arinze, Prefect of the Congregation for Divine Worship and the Discipline of the Sacraments responded on June 5, 2003, (Prot.n. 855/03/L).
The July 2003 Newsletter of the Bishops Committee on the Liturgy (BCL) noted the "controversy … over the proper posture of the faithful at Mass after receiving Holy Communion.
“In several dioceses people have been instructed that they must stand until the last person has received Communion, despite the long-standing custom that people knelt during the distribution of Communion”.
“Numerous inquiries” received by the BCL led Cardinal Francis George, chairman of the BCL, to submit a dubium (doubt, question) to the Holy See’s Congregation for Divine Worship and the Discipline of the Sacraments (CDW) on May 26, 2003:
Dubium: In many places, the faithful are accustomed to kneeling or sitting in personal prayer upon returning to their places after having individually received Holy Communion during Mass. Is it the intention of the Missale Romanum, editio typica tertia, to forbid this practice?
Cardinal Francis Arinze, Prefect of the CDW, responded to the question on June 5, 2003 (Prot. N. 855/03/L):
Responsum: Negative, et ad mensum [No, for this reason]. The mens [reasoning] is that the prescription of the Institutio Generalis Missalis Romani, no. 43, is intended, on the one hand, to ensure within broad limits a certain uniformity of posture within the congregation for the various parts of the celebration of Holy Mass, and on the other, to not regulate posture rigidly in such a way that those who wish to kneel or sit would no longer be free.
The BCL Newsletter continues: “In the implementation of the General Instruction of the Roman Missal, therefore, posture should not be regulated so rigidly as to forbid individual communicants from kneeling or sitting when returning from having received Holy Communion”