On one hand, this sounds reasonable apriori.

On the other hand, making games "fuzzy" to solve bargaining has been tried, and it's not enough.

On the third hand, I feel that some games might be genuinely indeterminate because they abstract too much, they don't include enough information from the real-world situation - information that in practice ends up determining the outcome. For example, (instantaneous) bargaining in the Rubinstein model depends on the players' (temporal) discount rates, and if you forgot to look at them, the instantaneous game seems pretty damn indeterminate.