We play as the copy V so that the game has some kind of ending and doesn't just black screen at Mikoshi. You don't even play as only V throughout the whole game, anyways, so I don't think the continuity of "still playing as V" matters.
Data doesn't move. Data is only copied and deleted. If the mind was "digitized", it's now data and subject to those facts.
Something I've not been able to get out of Soulkiller deniers, what do you think the bad thing about Soulkiller is, then? Alt says you'll lose something critically important. The reaction to having Soulkiller used on you in the net without your consent is obviously considered even by V to be a bad thing. What's the downside to Soulkiller?
I think the discussion needs to move past this point, as a solid conclusion cannot be reached, since it's become more of a philosophical question about the consciousness versus the soul. Regardless my whole point was, soulkiller or not, V and in proxy us, have been subjugated and defeated by the story at every critical point so far. So really the people who say we want a happy ending or something along those lines don't have solid grounds to stand on. We don't want a happy ending, I just feel that V needs a win. For her, for us.
Even as a character V is a massive asset to both fixers and corpos in Night City. She's arguably the most talented merc in the city on the road to become a legend and the whole merc angle works great with the open world nature of the game, but at this moment it's completely overshadowed by the story. V doesn't need to beat Arasaka, but she does need to win over this death sentence and come back stronger, be the merc she was supposed to be, not a play thing in the Arasaka power struggles. Which is what both V and Johny are. Ultimately whatever happens, it's about who sits at the throne of Arasaka and I don't think that even Corpo V cares at this point.