Yes, agree with all of this. Also:
Remove 'anxiety' as a reason for claiming disability and/or PIP or whatever the benefits are called.
Introduce proper IDs so that people can't so easily 'slip through the net' (and for those opposed to digital IDs, did you know that the UK is already Big Brother - more CCTV and facial recognition programmes than in most countries).
Proper IDs would mean it's easier to (a) catch benefits fraudsters, (b) ensure everyone pays tax (individuals and businesses - there is a huge black economy in the UK) and (c) would mean it's easier for employers to ensure they are employing only those who are here legally.
Increase income tax for ALL - the tax burden for average earners is one of the lowest here; we can't expect a Western European-style funded public service and welfare system whilst wanting US's low taxes!
Introduce a small charge (with a 'ceiling' for those who have chronic illnesses, are elderly or undergoing treatment for e.g. cancer) when you use the NHS - would stop misuse.
Increase unemployment benefits so that people aren't 'tempted' to seek for disability payments in order to survive (and once you're on benefits it's difficult to wean off them).
Reform of the triple lock pension (it's not sustainable) and public sector pensions.
Reform state pension so that people who have only ever worked max 16 hours (or whatever the minimum hours needed is) can get full state pension.