Sorry, no LH DEs yet. Those largely empty fields on the Liberty Head DEs (unlike the Saints) lend themselves to some shots at PL and DMPL (?) status. Anybody wanting great information on their Liberty Head Double Eagle year/mintmark...Doug Winter's website has lots of great information, plus he has an "online e-book" with year-by-year analyses including comments from other professionals like David Akers.
Here’s the very first liberty I bought which is a 1904 not a PL but still a nice coin purchased through a dealer choice I was really shocked when they gave me the most common coin out there….LOL
It has less to do with the large empty fields. It's more about the radius of the fields. On a Liberty Head, it has a smooth, shallow radius (depth) of the fields. On the Renaissance coinage (Buffalo nickels, St. Gaudens, etc.) they have much deeper fields, but also tend to have non-uniform radii. Based on the position and orientations of the main devices, the curvature might be a bit different in the left vs. right fields to maintain the effect of depth. Think about polishing a bowling ball (uniform radius) and tumbling rocks... one is much easier to get PL fields than the other.
This 1861 double eagle was issued in the early days of the Civil War when the both sides thought it would be over quickly, and the Union thought it could finance the war with gold. The results were high gold coin mintages in 1861. NGC graded this piece AU-58 over 25 years ago. I've seen many Type I double eagles graded Mint State that I didn't like as well.
That is my choice for a coin with uniform fields/devices, but most that I've found over the years were graded MS62 and MS63. I had one that was an awesome SEGS PL62 that had flawless uniform lustrous fields that I removed from the slab, sent with a lot to PCGS, came back "cleaned". I haven't sent anything to PCGS since, buying everything "sight-seen/slabbed".