There is no question that it is perfectly acceptable to appoint a shaliach (messenger ) to deliver the divorce document (get). The Rambam (Mishne Torah Gerushin chapter 6) writes
(6:3) A husband may [...] appoint an agent to deliver a get to his
wife. Such an agent is referred to as a delivery agent (sh'liach
holachah). (6:13) Until the get is given to the woman, the status of
the divorce is in doubt. Once it reaches her possession, the divorce
is definitely binding.
Now the question is whether to write a get is a mitsva. I originally thought it was (based on the Rambam's intro to Sefer Gerushin). When I discussed your question with R Binyamin Tabady, he mentioned the Maharsha writes that it is only a mitsva if the woman behaved improperly (e.g., relations with others), otherwise writing a get is permitted but is in no way a mitsva.
If it is a mitsva, we can build on the gemara in Kiddushin 41a which writes
it is more fitting that the mitzva be performed by the man himself
than by means of his agent.
as well as the gemara in Baba Kama 9b which writes that
what Rabbi Zeira said is that for the embellishment of the performance
of a mitzva, e.g., to purchase a more beautiful item used in the
performance of a mitzva, one should spend up to one-third more than
the cost of the standard item used to perform the mitzva.
to suggest that there is a hiddur mitsva (beautification of the mitsva) to do it in person.
But if the divorce is due to personal preferences, e.g., lack of fit between the spouses, then these gemarot don't apply and there is no benefit to giving the get in person.
In all cases, a rabbi who knows the couple should be approached to balance the above sources with his knowledge of the specifics of the situation and help come to a practical decision.