I'm not sure how to interpret your question.
If you're asking:
"What is the case against the MWI interpretation of quantum theory?"
then I would probably cite difficulties in explaining why our branch's history appears to be Born-rule typical as a major argument.
If instead you're asking:
"What is the case for a non-ontological interpretation of the wavefunction?"
then the best I can do is attempt to summarise the arguments put forth in the above papers.
I meant the second. If that is the point of the papers, then I guess that's fair enough, but, well, I don't anticipate that their argument is going to be valid. I'll go and read it; no need to summarize.
First paper,
The trouble with all these interpretations [Bohm, spontaneous collapse, WMI] as quick fixes for Bell’s hard-edged remark is that they look to be just that, really quick fixes.
I recognize that this is subjective and fuzzy, but... no? Bohm looks like an incredibly... well, I won't get into that, but it doesn't seem to me like a quick fix. Spon...
Sean Carroll, physicist and proponent of Everettian Quantum Mechanics, has just posted a new article going over some of the common objections to EQM and why they are false. Of particular interest to us as rationalists:
Very reminiscent of the quantum physics sequence here! I find that this distinction between number of entities and number of postulates is something that I need to remind people of all the time.
META: This is my first post; if I have done anything wrong, or could have done something better, please tell me!