No, it wouldn't. I did explain. Couples choosing to combine finances (example one worker and one parent at home) could choose to transfer non-working person's allowance to the worker. As they see fit. But opt-in, so nobody forced to combine finances. Either could revoke with a simple form online even if they did combine, so total autonomy. Lower earner in a couple if decide not to transfer allowances would be taxed exactly as they are now. No impact on couples at all except the added benefit that as in Denmark currently if they wanted to transfer allowance between them they could. Whether they did or not, their total allowance for the household would remain as now. No disadvantage to anybody in a couple. Some optional increased benefits. But no problem with keeping finances separate if chosen. The argument to disadvantage single parents to protect "financial independence" of women in couples is so obviously false, not necessary. I question the motives to make this argument as clearly that is not part of the change being discussed at all.
It would just be adjusting tax %s applied to single parents - so not changing the tax arrangements of couples - they would not be taxed a higher % on the same household income, taxed just as they are now. As you said before a single person will obviously have higher outgoings per person because they pay for a whole household and bills alone. That is fine and expected. What they should not be having is also being taxed more on the same income so they have less net pay to start with from the same household earnings, then trying to pay all of those double expenses (that a couple will split in some way) from a lower amount of after tax pay than the couple can keep when the couple earns the same amount. That "double whammy" makes it almost impossible to do successfully. Hence the high amount of poverty and lower outcomes for those households. Is this what we want, to make those households so poor they rely on welfare long term or can't work more or end up with poor health etc.?
You compound that problem if eligibility for things like child benefit or childcare are also based on a single income not household income. So "triple whammy". If they must be means tested then household income would be much fairer, but as explained before cheaper and better outcomes not to means test these for any family regardless of couple/ single. It costs more money and you then spend money on funding staff at DWP and HMRC instead of giving the money to children. Makes no sense.
Why would people want to charge a household more tax for the same income if it is already at a disadvantage of having only one parent and less adult time to split between earning or looking after the children? Couples who both work get twice the tax free allowances, can earn twice as much before they pay higher rate tax or lose their personal allowance, yet still can share childcare between them even if both working full time. To tax a single parent the same as them on the same household income still gives them a big advantage, just would avoid "stamping down" on the single parent even more on top of the inbuilt disadvantage.
In some couples where one works and one not, allowing the transfer of tax allowances if they wish would put them in the same position as those who both work and respect that it's up to families to make this decision, from the outside it should be identical: same household incomes attract the same tax. Then single parent should get the same allowances as the couple however they split them (or choose to keep them separate!), so that the same household income means the same amount of tax. It really isn't complicated and it is so obviously much fairer, I do not understand why anybody would have an issue. The single parent doesn't have the benefit that couple with one who works and one not working has, of one parent at home full time so no childcare cost, so will still be worse off. Don't worry no single parents will suddenly be getting an advantage over others! The two working parent family still has an advantage with two people to earn more, two people to share childcare. The couple with one worker has a worker who can work without restrictions on time due to childcare and no childcare cost. And both get to split costs as they wish when the single parent will pay alone. Because as you say of course living alone it costs more, and this is fine. But that cost should hit once, not three times compounded and then taxed more as well for the same household income! That is absolute madness. I don't see how any rational person could think that is fair. Or crazy to suggest households be charged the same on the same income no matter what their setup. It's not a "tax break" as somebody said, just basic fairness.
If we want these families of single paremts to be able to provide better for themselves, have better outcomes, need less welfare, then why would people not give them a chance to do that and "level the playing field" to get rid of the poverty traps shown in so much research on the UK system. It will still be much more expensive for them and always will be but insane to also penalise them through higher % tax on top, then people complain many don't work/ work enough.
UK system seems designed to make that not possible for them. Will never be the same as having two adults and will always cost more and that is understood but why design a tax system to make another level of disadvantage on top?
Easy fix that many countries do. Have explained the different approaches and what has been shown to work. Won't impact you if in a couple except over time there will be more tax revenue so you will get better public services or lower taxes. Or maybe UK Government will spend it all on broken PPE or moats or something but in any case single parents and their children would have better lives at no cost to you.