The US Philippine Proofs are widely sought after by collectors for their extraordinary beauty and scarcity.
One reason they're so sought after is the strike. The business strikes for the US Philippine series are notoriously weak and often don't capture the full beauty of the designs. By contrast, the proofs tend to be exceptionally struck. They do evoke the true beauty of the original design.
The US Philippine proofs were only minted for 5 years. In three of those years the mintages were 500 or less. So they're comparable in rarity with the rarest 20th Century US proofs.
Moreover, many of those proofs were damaged by the hot, humid weather in the Philippines and by the one-time propensity of the Philippine dealers to clean their coins to achieve a bright shiny look which they thought their customers preferred.
So the number of survivors is quite small. For instance, PCGS has certified only 25 1906 50 centavo proofs and 13 1908 peso proofs as gems. And the bronze 1/2 centavo and centavos are extraordinarily rare in gem RED. PCGS, for instance, has graded only 8 1904 centavos in gem red.
In 1908, the size of the silver 10 centavo, 20 centavo, 50 centavo and peso proofs were reduced. Since 1908 was the last year of issue for the US Philippine proofs, the size reduction created an interesting one-year type coin. Total mintage is only 500, which makes it one of the scarcest years. And the added demand from type collectors has set a premium on their value.