Yes in it's essence PWT doesn't conflict with the concept of strings (nothing really does), I'm not so sure that I doesn't conflict with the leading "complete" string theories out there today.
But most interpretations have the same statistical predictions as standard QM. The standard Copenhagen setup can be argued to not actually be a theory (the split between quantum and classical in a fundamental theory is an absurdity since the classical is made up of quantum ), but assuming that an interpretation is clear enough to be called a theory and has the same statistical framework as standard quantum mechanics, then experiments will not distinguish them.
The different interpretations, however, may lead to different insights for extending the theory. And in that game, one may pull ahead of the other. For example PWT inspired Bell's results. PWT can also explain the impact of the topology of configuration space convincingly since the configuration is a fundamental part of the theory. It leads to many insights that the others just have to assume.
GRW with a flash ontology has a relativistic version with no foliations. So that's cool.
Of course, the PWT viewpoint may suggest new ideas and understandings; it is, after all, what led Bell to his inequality and thus spawned all of the entanglement uses including quantum cryptography. But it gets reincorporated into standard quantum mechanics.
None of that really matters. People reject PWT because they want to reject it. There have never been any good reasons. It is an extremely simple theory that answers the questions.
If it gets accepted in the future, it will only be because of a new generation being more willing to embrace it.
At first the physicists said it was impossible and then when it was obvious that it was possible, they said it was too trivial. This is a hallmark of reason being used to justify an already decided on outcome.
It is also not in conflict with string theory. One could imagine string theory actually having strings that evolve. This would be the spirit of PWT applied to that realm.