Receiving Communion under both species was common in earlier times. There was a time when it was even mandated as a response to a heresy, because false Christians refused to receive under the form of wine.
There is nothing lost in receiving under only one species. The only difference between receiving under ONE species or BOTH is that the visible sign value is more apparent to the one receiving.
When you receive under the form of bread, you receive the Precious Body and the Precious Blood; the same goes for the form of wine.
The Council of Trent decided not to change the discipline, but left it to the Pope for future consideration. Vatican II promoted the concession of the chalice, but only on very specific occasions. This has been superseded by common practice (especially in the US), probably to the general detriment of the understanding of the doctrines concerning the Eucharist.
Consider 1980’s Inaestimabile Donum 12:With regard to Communion under both kinds, the norms laid down by the Church must be observed, both by reason of the reverence due to the Sacrament and for the good of those receiving the Eucharist, in accordance with variations in circumstances, times and places. Episcopal conferences and ordinaries also are not to go beyond what is laid down in the present discipline: the granting of permission for Communion under both kinds is not to be indiscriminate, and the celebrations in question are to be specified precisely; the groups that use this faculty are to be clearly defined, well disciplined, and homogeneous.
That was widely unheeded. Eventually Rome capitulated to bishops who were either disobedient or unable (or unwilling?) to correct the situation in their dioceses.