This proposal (PPP) makes decent sense in a unicameral context, but most of the US is bicameral - literally the only exception is Nebraska.
In a bicameral legislature, there is an opportunity for the chambers to specialize. For example, the lower chamber might be comprised of seats for single winner constituencies, while the upper chamber might be proportional. The advantage of this is you don’t have to compromise the effectiveness of local representation to produce proportional representation (and visa versa).
In the US, I think the Senate is better situated for regional representation, while the House is better for ideological representation. I’d want Senate seats elected using Approval voting, in order to maximize the broadness of their support within their own state. That way ideology takes a back seat to state-level concerns.
In the case of the House, the goal should be ideological proportionality within each state delegation. However, there are some significant barriers to this goal. First, the Uniform Congressional District Act of 1967 needs to be amended to allow at-large and multi-member districts, when a proportional method is used. Second, a proportional method is not possible for many small states, due to only having one or two apportioned seats. The Permanent Apportionment Act of 1929 would have to be completely repealed, and the House expanded, so states like Wyoming, Delaware, and Alaska could send reasonably proportional delegations. But I won’t advocate a specific proportional method, since I think it is reasonable to leave that up to the states themselves, for experimentation.
With that context, I am inclined to say PPP, though likely well suited to the UK, is likely not a great fit for the US. However, my mind could be changed if you can think of a secondary system that would compliment PPP well in a bicameral setting (i.e. if a state used PPP in its House, and something else in its Senate).