Should
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A new player relation called "myself" be added;
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the client automatically tag your own characters (the ones you logged in on) as "myself" relation;
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the client unconditionally allowing and accepting trade requests from characters tagged with "myself" relation;
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trading with a character that has "myself" relation would no longer feature the "agree" step. Instead, there would be a combined "propose and agree" button.
This would reduce trading items between your own (tagged as "myself") characters from 9 steps (right click trade -> switch to the other window -> accept trade request -> propose -> switch to the first window -> propose -> agree -> switch to the other window -> agree) down to 4 (right click trade -> propose and agree -> switch to the other window -> propose and agree).