The answer is NOSTALGIA and an appreciation of the dart like sleekness of the cartridge/bullet and the attitude towards quality by expert craftsmen that made the rifles to shot those Wildcats which were latter adopted by major rifle manufacturers!!!
The really old 25 Neidner (standard 25-06) was the first SPRINGFIELD 30-06 (1906) wildcat made by simply reducing the neck!!! Standing a 25-06 up to a 30-06 loaded rounds, one would choose the 25 cal because it looks balanced!!! And when you reload for both cartridges, you look at that sleek, dart like 25 cal bullet and wonder why you still have the 30-06 around?? That cartridge and rifle do have sedimental value too me!! My 25-06 was my 1st custom build over 40 years ago!!! It is a battlefield proven (both WW1 and WW2) tough and reliable Springfield 03A3 action make specifically for the 30-06 cartridge!!
NOTE: Of all the AI cartridges PO Ackley designed, his favor round was the standard 25-06 (slightly over bore) where he ADMITTED the 25-06 AI is way over bore and the added powder charge was a waste with very little gain in velocity!! Ackley also stated the same with the 6.5-06 (at bore) vs 6.5-06 AI (over bore) with the same length barrel comparison!!!
The 256 Newton was developed prior to WW1 and factory ammo was available up an till WW2 when that cartridge died out! Factory made rifles were also made for that cartridge!! If memory serves me right, the parent cartridge was the Springfield 30-03 (1903)!!!
The Rem 22-250 (ak: 22 Varminter, .220 Wotkyns Original Swift (.220 WOS)) are also another old time wildcat made from the 250-3000 Savage (1914). The 220 WOS was slightly different than the simple necked down 22 Varminter!! For all practical purposes, the reloading data was the same for both expect for reduced loads, which the 22 Varminter being the better option!!! Once again, stand the reloaded 22-250 up next to it patent cartridge, the 250-3000 Savage, one would pick the balanced, sleeker 22-250 with slender dart like bullets!!! My go to, but lightly shoot out rifle is a REM 700 VLS!! It has a barrel code dating stamp being one year prior to the release of the 1st year production/REM sales VLS run!!! I TEND TO SPECULATE IT WAS A SHOW, DISPLAY, PRE PRODUCTION RIFLE WITH THE ADDED FACTORY CHECKERING!!!
One of my favorite and oldest rimless bottleneck cartridge is the 6.5x55 SWEDE (1894)!! My old C/R M96B Swedish Mauser (1917 all matching numbers) was designed to shoot a 156 grain bullet at 2460f/s out of the long (29.5") military tapered barrel and loves the 139 and 140 Darts!!!! It is fun to shoot long distance plinking with very little recoil!!
If I want to get into more serious open sight plinking, out comes my now antique, CROWNED JEWEL OF SWEDEN, CG63 target rifle ((1965) a factory modified M96 action (Mauser designed small ring receiver), milled and polished sears which reduces lock time, cut off pull/lock firing pin knob, wide ribbed tuned target trigger, 29.5" Norma Palma barrel, mounted on a Birchwood target stock)!! This rifle is extremely rare (1900 German made Swedish pre production receiver) and I always wanted to know what the full accuracy capability would be by mounting a target scope!! BUT, no modifications will be done on that gun!!! It is extremely valuable and part of my investments!!!