I happen to have notes on the grasses planted at Ballyneal and Chambers Bay, which were built at about the same time.
Ballyneal greens were planted with two types of fescue (red and Chewings) (total of 70%) and browntop bent (30%).
Chambers Bay was planted with two types of fescue (red and Chewings) (total of 90-95%) and browntop bent (5-10%).
Adding to the information, the experiences at Bandon caused the resort to reduce the percentage of bent in the grassing mix to be reduced from about 8% at Bandon Dunes and Pacific Dunes down to 0% for Old Macdonald.
In all these cases, Poa annua eventually encroached on the playing surfaces. At Ballyneal, the encroachment took a couple years longer to make a significant appearance (say 5-10% of the total surface). Ballyneal is a harsh, arid environment, less hospitable to Poa, and therefore the effort to overseed the greens with bent has been quite successful. I would now estimate the Bent - Poa - fescue percentages to be something like 60-20-20, and they now putt more smoothly than they have since the first couple of years, when the greens were smooth and slow.
My experience as a longtime member at Pumpkin Ridge in Oregon informs my opinions about Poa infestation. The club opened in 1992 with pure Penncross bent greens; by 1999 Poa percentages in the greens were increasing exponentially. After fighting the infestation for one year, the club wisely decided to encourage the establishment of Poa on the greens. After a two to three year transition period, the greens improved year after year, and after 26 years the greens are now superb putting surfaces, fast and smooth, easily groomed to increase putting speeds as needed.
The current superintendent a Pumpkin Ridge has done something to encourage bent in the fairways, and it has been somewhat successful. It must have something to do with the length of grass that makes bent more competitive in the fairways.
Similarly, Bandon Dunes and Pacific Dunes briefly fought the Poa, then modified their practices to encourage it, and now the greens are in good shape again. Bandon Trails is in the late stages of the transition. I'm sure our weather is substantially similar to England, but the general rules in the Pacific Northwest seems to be: 1) until recently(?), the initial seeding of a golf course could not be done with Poa, 2) Poa starts appearing significantly on the greens within 6-8 years, during which time the grass has poor characteristics for putting, and 3) within a few years, the Poa plants begin to adpt to the low mowing environment and create a fine surface for putting well suited to the environment.
Here in the Pac NW, until further notice, humans cannot prevent Poa annua from dominating golf courses, especially the greens.