Sure, if you or I felt like going through quite a bit of effort and legal fees to do it, because there's no good reason anyone would expect that you would want me to make those decisions for you. In the case of a same-sex couple, who have joined their lives just as thoroughly as an opposite-sex couple in every way but legally, that absence of reason isn't there.
And I think in some cases they're being treated that way - all the states that have bans on "marriage-like benefits" for unmarried couples spring to mind. However, I consider treating these rights as "incentives" as something awful. In many cases, it amounts to taking an unfortunate, unexpected event and making it even worse.
Put yourself in a situation that happened to some friends of mine recently: the husband had a very severe (and unexpected) respiratory attack. The doctors induced a coma while the damage of the attack could be repaired and healed; he was unconscious for more than a month, and unable to talk for a month after that. While dealing with all this as well as their two little girls, his wife also had to arrange with the bank to get into the accounts in his name to make sure that the bills and mortgage would get paid. Because they were married, she was able to do this.
Now... still imagining yourself as the wife, change it slightly: rather than giving control of your husband's accounts to you, the bank gives control to a vindictive relative of your husband who thoroughly disapproves of your relationship. How do you think things would play out? Do you think the result would be good, right, fair or just?
I think that denying people this sort of an ability doens't provide an "incentive"; it kicks them when they're down.