There are probably as many purposes with flats as collectors existing. Besides a certain interest in history, there are 4 basically different interests regularily connected with flats collecting:
Dioramas - Many collectors paint their flats to build a diorama of any historical event choosen. There are thousands of them existing in Germany some hundred assembled at the Flats museum located in an cstle, the Plassenburg at Kulmbach. There are dioramas of battles (Leuthen, Leipzig) which consist of 30-40.000 flats alone.
Painting - Some collectors are "just" painters and choose their flat irrespective of epoch for the beauty of the subject, assemling them like some special kind of picture.
"Stamp-collecting" - Some want to have just all flats of a certain epoch, designer, engraver, editor or subject for instance collecting all coaches ever edited with flats.
- Some collectors assemble huge armys of flats to fight virtual battles with fellow collectors. This was popular in Germany before WWII but is rarly to be found today. You may find a sample here
My personal interest is concentrated on both painting and "stamp collecting" as I try to collect for example all flats engraved by L. Frank, at least of Napoleonic era.