I understand your theory but it's not backed by data. Do you have survey data that people want to work more hours? If surveys don't suggest that this is the case, then we could suspect that workers are on the steep part of the income-leisure indifference curve, and income would have to be bumped up a lot more than your tax proposition would for workers to give up more leisure time.
In addition to workers working long hours being less productive, you'd also send workers into fields where they have less expertise, which further reduces their productivity. Part-time jobs aren't exactly known for being jobs with high productivity either.
Taxman is not going to clock that you worked six hours instead of eight and then worked two hours doing the same tasks at "the second job". New biz will also have huge tax advantage over established businesses. Let's ask construction and hospitality industries how they feel about competitors whose employees don't pay taxes.
Most people in the UK will work more at the moment, with high mortgage payments and a real term fall in pay. Not only do you get a second personal allowance with the SASI but the tax rates start again for the second business.
In terms of productivity if more is produced productivity is increased on a macroeconomic level even if an individual worker is producing a lesser hourly rate, as long as they are working more the overall economy is still growing. Individual productivity may fall.
In the UK you have to register each business independently. Each business has to be stated in the annual self assessment form and then details of its operations have to be put in. You would get a second personal taxation allowance for the second registered business.
In terms of getting round paying tax. That is exactly what I am trying to do. I am trying to build a second legal System D economy on top of the existing taxed economy. As long as the new economy does not affect the existing economy it will work.
You can only get the second personal taxation allowance if you are in and remain in primary occupation. Primary Occupation is the occupation generating the greater amount of income. Most Primary forms of occupation will require a minimum number of working hours.
It is hard to get around employment regulation on the part of the employee in the UK. By offering this new supplementary form of income or treating supplementary income differently in the taxation regime will massively benefit people on low incomes who could earn more.
Getting two part time jobs and two personal allowances is good. Most part time jobs on their own will not surpass the primary or secondary allowances and each occupation cannot use the others allowance. It is similar to a separate entity you can draw tax free income from.
You do not get £23,000 of allowances. One occupation gets £11,500 and the second occupation gets the other £11,500. Most part time jobs will not generate over that amount so I think it is unlikely someone in full time occupation will take two part time jobs to avoid tax.
You would be limiting yourself to £23,000 of untaxed income instead of whatever you would get for full time work, you also assume they would be able to get the exact amount of part time work they would need to reach that amount.
Most people in part time work lack job security so they will lose a lot by not working full time. The supplementary allowance will help people who cannot get full time work receive some compensation for the losses of not being in full time work and could make it similar.
It might be worth someone in part time work taking more part time work, which would not impact existing tax intake. It might be worth someone in full time employment taking part time work or starting a business and not impact existing tax intake. Output would increase.
In terms of people wanting more work. Yes I think they will want it due to the increase in pay disputes and real incomes falling. Most people will want to work their way out of poverty if they can. This is a way of enabling, what could be minimal extra work for a lot more reward.
You are also assuming the whole thing is about jobs. It is not, starting and operating a business if different from working for someone else. You could perform independent trade and not have to pay tax on it up to £11,500. Think System D but legal. Is time an issue?