Oh boy, there could be volumes written against this. Unnecessary is not a word I would use, and frankly it’s an extremely problematic mentality that was unfortunately propagated in the West until Pius XII’s Mediator Dei. It seems quite intuitive that the confection of the Eucharist is for its reception - perhaps not by everyone all the time but to received by all who are able sometimes. The corpus of Patristic literature on the spiritual advantages of receiving the Eucharist express its reception as quite necessary, in fact. The institution narrative even states it is given for many not one.
Receiving under one kind is not normative, at least in the US. There exists a document called the Norms For The Distribution And Reception Of Holy Communion Under Both Kinds In The Dioceses Of The United States Of America. Furthermore, the communing under a singular species is a liturgical aberration that the novus ordo sought to correct (whether or not the method employed is perceived as proper) - essentially since the Latin commingling during the fraction only goes one way. The inconsequential attitude some Latin Catholics approach the Blood with actually shocks and mortifies Eastern Christians.
Re OP: All that being said, the priest should really either commune as many laity as possible with the blood or singularly himself. It seems the only actually legislated rule, though, is that it is fitting that all concelebrants be communed with the Blood.
(a) In reference to the Eucharist as a sacrifice, the communion, under both kinds, of the celebrating priest belongs at least to the integrity, and, according to some theologians, to the essence, of the sacrificial rite, and may not therefore be omitted without violating the sacrificial precept of Christ: “Do this for a commemoration of me” (Luke 22:19).
This is taught implicitly by the Council of Trent (Sess. XXI, c. i; XXII, c. i).
(b) There is no Divine precept binding the laity or non-celebrating priests to receive the sacrament under both kinds (Trent, sess. XXI, c. i.)
(c) By reason of the hypostatic union and of the indivisibility of His glorified humanity, Christ is really present and is received whole and entire, body and blood, soul and Divinity, under either species alone; nor, as regards the fruits of the sacrament, is the communicant under one kind deprived of any grace necessary for salvation (Trent, Sess. XXI, c., iii).
(d) In reference to the sacraments generally, apart from their substance, salva eorum substantia, i.e. apart from what has been strictly determined by Divine institution or precept, the Church has authority to determine or modify the rites and usages employed in their administration, according as she judges it expedient for the greater profit of the recipients or the better protections of the sacraments themselves against irreverence.
Hence “although the usage of Communion under two kinds was not infrequent in the early ages [ab initio] of the Christian religion, yet, the custom in this respect having changed almost universally [latissime] in the course of time, holy mother the Church, mindful of her authority in the administration of the Sacraments, and influenced by weighty and just reasons, has approved the custom of communicating under one kind, and decreed it to have the force of a law, which may not be set aside or changed but by the Church’s own authority” (Trent, Sess. XXI, c. ii).
Not only, therefore, is Communion under both kinds not obligatory on the faithful, but the chalice is strictly forbidden by ecclesiastical law to any but the celebrating priest. These decrees of the Council of Trent were directed against the Reformers of the sixteenth century, who, on the strength of John 6:54, Matthew 26:27, and Luke 22:17-19, enforced in most cases by a denial of the Real Presence and of the Sacrifice of the Mass, maintained the existence of a Divine precept obliging the faithful to receive under both kinds, and denounced the Catholic practice of withholding the cup from the laity as a sacrilegious mutilation of the sacrament.
