Could we use a new starter? Yes? Although doesn't each reprinting include all of the latest errata and such so it essentially is a "new" starter that happens to functionally look just like the old one.
Could we use a Deluxe Starter with improved templates and alternative models of the TIE and X-WING? Here I'd give an even bigger YES although everything in it would be optional to someone who already has the stuff needed to play.
Could we use an Alternative Starter? As in one that uses a different mix of ships and upgrades. This could be used but it would need to be pretty specific to avoid alienating the player base. I somewhat like the idea of creating a "Faction Primer" set that includes "the basics you need to get started in X-Wing playing for a given faction." The problem is it may not make finacial sense for FFG unless they add new stuff so everyone buys it which then upsets the current player base.