I find this idea intriguing too! The idea that time emerges from entanglement is mainstream enough to have a 2014 article in Quanta Magazine on the topic, "Time’s Arrow Traced to Quantum Source". Here is an excerpt:
In 2009, the Bristol group’s proof resonated with quantum information theorists, opening up new uses for their techniques. It showed that as objects interact with their surroundings — as the particles in a cup of coffee collide with the air, for example — information about their properties “leaks out and becomes smeared over the entire environment,” Popescu explained. This local information loss causes the state of the coffee to stagnate even as the pure state of the entire room continues to evolve. Except for rare, random fluctuations, he said, “its state stops changing in time.”
Consequently, a tepid cup of coffee does not spontaneously warm up. In principle, as the pure state of the room evolves, the coffee could suddenly become unmixed from the air and enter a pure state of its own. But there are so many more mixed states than pure states available to the coffee that this practically never happens — one would have to outlive the universe to witness it. This statistical unlikelihood gives time’s arrow the appearance of irreversibility. “Essentially entanglement opens a very large space for you,” Popescu said. “It’s like you are at the park and you start next to the gate, far from equilibrium. Then you enter and you have this enormous place and you get lost in it. And you never come back to the gate.”
In the new story of the arrow of time, it is the loss of information through quantum entanglement, rather than a subjective lack of human knowledge, that drives a cup of coffee into equilibrium with the surrounding room.
The article credits Seth Llyod with the idea that entanglement drives the arrow of time. No mention is made of Page or Wootters.
However, the Wikipedia entry for Quantum Entanglement mentions both Page and Wootters and Llyod regarding the relationship between entanglement and time:
There have been suggestions to look at the concept of time as an emergent phenomenon that is a side effect of quantum entanglement. In other words, time is an entanglement phenomenon, which places all equal clock readings (of correctly prepared clocks, or of any objects usable as clocks) into the same history. This was first fully theorized by Don Page and William Wootters in 1983. The Wheeler–DeWitt equation that combines general relativity and quantum mechanics – by leaving out time altogether – was introduced in the 1960s and it was taken up again in 1983, when the theorists Don Page and William Wootters made a solution based on the quantum phenomenon of entanglement. Page and Wootters argued that entanglement can be used to measure time.
Physicist Seth Lloyd says that quantum uncertainty gives rise to entanglement, the putative source of the arrow of time. According to Lloyd; "The arrow of time is an arrow of increasing correlations." The approach to entanglement would be from the perspective of the causal arrow of time, with the assumption that the cause of the measurement of one particle determines the effect of the result of the other particle's measurement.
Unfortunately, I can't tell from such descriptions the degree of similarity between Page and Wootters theory and Llyods theory.