The problem with that idea is that it's not universal for all Shepards. Aside from practical concerns like it doubling the memory budget by having to record the dialogue twice, what if you're playing a full on renegade that doesn't feel at all bad about the loss of Kaiden (I know I didn't!) It also risks alienating anyone who hasn't played the previous games as they'll have no clue who that person is, nor why they should care. Plus of course this would place that particular character's death as "important" over and above anyone else who may have died since in ME2 & earlier in ME3, which again is not universal to all Shepards.
They spent a lot of time in the game establishing the recurring dream and what it means to Shepard. The kid is just a symbol. Indeed, after one of the dreams (the second one I think?) Shepard can tell Liara that she was thinking about whomever died on Virmire.
If you're a Renegade who doesn't feel bad about killing Kaiden, why would you care about a kid you have absolutely no connection with? If Shepard is worried about humans dying on Earth, why wouldn't she care about deaths among her own crew?
Kaiden/Ashley work precisely because it's the first "major" choice the franchise forces you to make. You can get out of killing Wrex, but you are forced into a no-win scenario that even Kirk couldn't worm his way out of on his best day, so it's something that's universal to all people who have played the three games.
As for new players? I don't think they would care about the story anyway.