If they're not married yet, what would the new wife expect? Before and after the new marriage are two different situations.
I think it would be a good thing for a spouse to pray for their deceased spouse. It shows the new spouse what they can expect if they die first -- they'll be prayed for and remembered! You can't beat that with a stick.
And unlike jealousy about a past "partner" who is still living (which must be awful -- wondering who they're with on this fine lonely night, etc.), it has to be different when the "previous" spouse is deceased. How can you be jealous of a person no longer among the living?
I think that's the worst thing about freely given annulments in the Conciliar Church -- it's so close to divorce, you have just as many "ex-wives" in the Novus Ordo pews as you have in a protestant church. And broken marriages are no small matter! We're talking about broken families, and destroyed bonds that were supposed to be permanent.
When a man and woman are intimate, extremely strong psychological and emotional bonds are formed. Such intimate bonds were not ever meant to be created with more than one person, as is the case today. No wonder the world is so messed-up.
So even if a person snags an annulment, he still might very well end up with "experience" with more than one (living) person. Don't think that won't lead to emotional and other consequences.
Grief has to be a lot different when a partner dies, vs. when a partner "leaves". When a partner is still alive, you can always hold out hope...
At any rate, the Catholic Church tends to agree. You can't marry more than one person, unless that first spouse dies.