Why can't I just do my taxes....with the software in a reasonable way....? Why? Why might I NEED a US phone number? US credit card?
Because, as you know, easily available software is designed for US residents with income reported to the IRS through W-2's, 1099's, etc. The software is not designed for anyone resident abroad, although with the workarounds it can be made, in many certain circumstances, to work adequately. There is no software specifically designed for USCs abroad which understands all their various incomes and foreign tax paid and works in all foreign countries (although there is software for pros to do this, but it's very expensive). There aren't enough USCs in the UK for a company to make a profit on a US/UK specific return.
If I cut off all ties to the US....how might I do my US taxes?
If you know which forms you will need (1040, Sch. B, 8938, 1116, etc.), simply google "form 1040" (or whichever) and download the PDF version of the form from the IRS site. With Adobe Acrobat you can enter all the information needed on the form. Print it off, sign it, and send it in. Job done.
Pros:
You only have to complete the information required, and do not have to create "funny" information, "funny" forms, and use "funny" methods which are solely needed to make the software work.
Negatives:
It takes longer and you will have to do all the math (and checking the math). Free File Fillable Forms evidently will also do some of the math if you use them.
The time required is maybe 30% longer, but you have to create the information to enter in both the software and on the forms. I believe that includes the apportioning for form 1116 for both. You will have to enter, many times, your name and SS number on each form. I believe the software does this automatically for each form. You'll also discover there are multiple ways to report income.