What does a tahara, the process of washing and dressing a dead person, accomplish spiritually for the meis?
Chazal has said that if we begin a mitzvah that we cannot complete on our own, G-d will complete it for us. We could not part the waters at the Sea, alone, but we had to take the first step into the water. See, e.g. Rashi to Exodus 14:15. Moreover, we accept that as mortal humans, we may not be perfect, per se, but that if we make efforts to seek perfect observance, G-d will deem us perfect. Psalm 19:14.
Similarly, during our lifetimes, we have the duty to cleanse ourselves, physically and spiritually, before standing before G-d in prayer. We at least wash our hands ritually. Many people go to the mikvah, even though the Temple is gone. And although we are not strictly as spiritually pure as we would like, we believe that G-d will complete our cleansing, as Isaiah saw in his vision of an appearance before Hashem's court. Isaiah 6:6-7. However, in death, when we are truly going to stand before G-d, we are unable to attend to our physical cleaning, therefore it is up to our friends and neighbors to assist us in that cleansing.
We see this in the quotation from Yoma 85b, that some chevra kadishas say during the Tahara:
"Rabbi Akiva said: Happy are you Israel. Before whom do you cleanse yourselves and who cleanses you? It is your Father, who is in heaven. As it is said (Ezekiel 36:25) “Then I will sprinkle clean water upon you, and you shall be clean from all your uncleanness and from all your idols I will cleanse you.” The Holy One blessed be He purifies Israel.
So, it would appear that although the deceased cannot himself, or herself, prepare his body to meet his or her maker, we grant them that final courtesy.