IMHO, the significance of the 5565 are:
- Stainless Steel Calatrava. Using SS for Calatrava model is rare. (It used to fetch high price in auction because of the "rarity")
- special 2-tone classic dial
- special military hands
- special crown for 5565 (retro-design)
- special no-bezel design
- the design is based on the famous 565 models.
565 was considered a large watch back then (35mm).... it was rare in that era.
Now PP is re-issuing a modern watch with similar design. It is considered small (36mm) today.... As a new watch, it is rare in our time 
A similar 565 was auctioned with a price of 82600 USD (including buyer's premium) .
pg
- Limited Edition (only 300 pcs were made)
(From the auction catalog: "To celebrate the re-opening of the famous Patek Philippe store on the Quai General Guisan, which had been closed for two years for renovation, Patek Philippe held a reception in December 2006 for their best customers. At this inaugural party, they also announced that two watches had been especially created: Ref. 5105 in platinum and Ref. 5565 in steel. Both watches were made in limited quantities; 100 examples of reference 5105 and 300 examples of reference 5565.")
- Difficult to get. They only sell the watch through the Geneva boutique to the clients they know
Facts:
List Price: CHF 19000 (~ 15368 USD)
Last Auction Price: 42480 USD (including buyer's premium)
I think some collectors are just focusing on the complication when they collect watches. However, IMVHO, I believe that a nice collectible watch is not just meant movement or complications... Once you becoming more and more experienced in collecting, you will think the movement/complication is just part of the watch; the design is actually also a major part for a watch
(In fact, there are limited different complications in watches... but the design for a watch is unlimited!)
Look at the 3712 vs 5085... you will know a great design can make a huge difference.
Yes, you are right. There is no complication in 5565. What it can give is "just" the plain beauty...
[The above photo is from the net...]