Means testing is fiendish, mainly because the UK has evolved a complex tax/benefit infrastructure.
Before anything else, you need to have accurate data for the time frame in question (so we're already holed before the waterline, because we haven't got that).
Then you have to assemble it to cover the financial year in question (remember you can offset allowances over previous or future years, depending on which area of the system you are looking at).
Then you have to aggregate household figures, where appropriate (and that'll be another hole in the data, given "household" is one of those irregular government nouns)
Then, and only then, can you decide if the person/household in question is eligible for the benefit in question. Or whether they need to repay a benefit, as they earned more over the year than the threshold (although when they claimed the benefit they were eligible).
Of course all of this has to be done in real-time (or as close to as possible) since it would be impossible to only pay benefits in arrears (imagine waiting a year until your benefit could be paid). And against a background of people moving, being born, getting married, divorced and dying (plus immigrating/emigrating) and a cornucopia of various methods of investing which may -or may not - affect benefits.
That's just a very high level view for starters.
If Universal Credit was going to work, it could address (some of) these issues. But it isn't, nor ever will, so we need to go back to the drawing board.
Means testing is one of those ideas which sounds fair, until you realise the enormous cost of administering it.
And note, I say "sounds" fair. Because invariably, you will hit situations - like the Lurking household - where a household earns £0.01 over the threshold, and then has to pay for things which a household £0.01 under the threshold doesn't have to. So because I earn enough that MrsLH can't receive IS, she has to pay travel, prescription, dental, and optical charges - a few hundred a year which then makes her worse off than someone claiming IS and getting free prescriptions, dental care, and optical care. Plus the wages I lose, having to drive her to (numerous) medical appointments. Plus the parking charges.
Yes, you could smooth things out with a taper. But since we can't administer the system we have, it's pointless adding more "what ifs".
And regardless of solutions, the current and planned situations are ideological, not practical. This government, despite all the AusterityBollocks, would happily burn a bonfire of pulped fivers if it ensured the Tory message was getting through load and clear. That's why no one really cares if the Bedroom Tax saves money.
But, as I say, the real news yesterday, was Jeremy Vine appearing on Strictly. So let's get back to that and stop wasting our time with things that will never change.