Not sure why a priest would do this, and I’ve never seen it done.
Jesus said, “take and eat,” then, “take and drink.”
As others have stated, intinction is indeed an option. It has some very limited utility. When I was on a medication that was to have no admixture with alcohol, as Presider at Eucharist I would intinct the portion of the Host I consumed so as to consumate the sacrifice by consuming of both species just consecrated – as required by sacramental theology – while consuming the tiniest tiniest possible amount of the chalice’s contents. The Deacon or someone else present would consume what was in the chalice.
At Masses of large concelebration, it is easier logistically for a variety of reasons as well as more expeditious for the concelebrants to use this method to communicate.
As for giving Communion to the laity of the West by this method…it leaves much to be desired.
As you indicate, the sign value of “Take and eat” then “Take and drink” is lost.
It necessitates receiving on the tongue, which needs to be avoided.
It presents a problem relative to children and the Sacrament.
It also creates problems relative to allergies and other sensitivities by distributing in this method.
Confronted with only the possibility of this option, I would choose to give only under one species and work expeditiously to resolve the matter in favour of having both species, separately offered, as soon as feasible.
Frankly, this comes up in liturgical conferences not infrequently. Many bishops will remark that, as supreme liturgists of their respective dioceses, they will let it be known to their presbyterates that this is not a desirable avenue for them to pursue.
