I don't think this has anything to do with remote vs. onsite work. It has more to do with remote vs. onsite interviews. A thorough onsite interview should catch all of these fake candidates. Companies should be doing at least one onsite interview regardless of whether the role itself is remote or onsite.
Only if they are 100% fake as opposed to farming out work to someone else. I can turn up to an interview in person no problem. When hired I just have the person in India use my name/picture and do the work.
Of course if they hire me as opposed to that person in India directly there is likely a reason they wanted someone in the US. Often those reasons are legal and somewhere a law is being broken.
By the time someone gets to the on-site interview, the job should be "theirs to lose." You wouldn't be spending the cost of an on-site trip for every candidate that shows some promise during the distance interviews--you'd do it for those very few you're ready to give offers to already, but just want to double check a few in-person soft-skills things (and now, want to double check that he is who he says he is).