I was with you until you got to PIP. There are certainly other countries in the world who have similar systems to PIP. France provides financial aid to cover additional expenses caused by a disability. It assesses a person's difficulty in everyday life similarly to the way PIP does here.
Denmark has an assessment system and offers monthly payments based on cost. Norway has several rates determined by the level of disability - similarly to the way PIP works. Sweden has a system of different rates, also based on levels of cost. Germany has a disability pension which is reviewed based on inflation and Italy has a disability benefits system based on cost of living. The USA and Australia have systems of disability benefits - some of which are means-tested and some of which are universal.
I worked as a disability outreach worker for over twenty years. The PIP assessment system is no more up for fiddling that any other system. Whatever safeguards you have in place, there will always be some who can get around them but generally fraud and error in the disability benefits system is less than one percent.
If the proposed cuts to PIP were centred around tightening of the rules and requiring more robust medical evidence for MH and spectrum conditions instead of allowing self identification, this would go some way towards bringing the costs down, as the rise has been proven to be as a result of the PIP system introduced in 2013 allowing claims for MH and similar conditions, where previously they were limited to physical disability with the exception of a very few MH conditions. The Equality Act 2010 determines that formal diagnosis isn’t necessary for someone to be considered disabled, and this has also led to an increase in claims.
Appeals are another area where bucketloads of money could be saved. At the moment the decision making process within the PIP system isn’t fit for purpose - many claimants are wrongly denied benefits and have to resort to costly tribunals to get a fair hearing. If the assessment and awards system was made fairer and more transparent it would eliminate the need for these tribunals.