I’m glad you said all this.
I was beginning to wonder, with the talk of ‘incomprehensible’, ‘pay day loans’ and ‘infinite leases’, if this was some other PCP that I was not aware of.
In the UK PCP is not only easy to understand but the sales agent has to also explain it to you anyway and you get to sign to say it was explained to you.
Your description is correct, I would just add that you often do not need to pay anything upfront, can choose how long the PCP period is (up to a maximum of, generally, 42 months), the interest rate can be 0% and at the end of the term you do not have to either buy the car of trade it in, you can just give it back.
Putting aside the debate of buying new or secondhand, if one does intend to buy new PCP at 0% is the best way to do it if you need to take finance.
It is popular in the UK as an alternative to a company car. Many UK firms will give a cash allowance option instead of a company car. Then it is a case of looking at tax on the cash as earnings vs. rising tax year on year on a company car as a benefit in kind. That is a lot more complicated to understand then the very simple PCP.