Yes! Cost. Retired tractor engineer here. You typically see sprung tensioners on high quality drives that
see variable loading. Why? The belt tension is held to a low constant regardless of the loading allowing long life for the drive.
Many belt manufacturers advise their V-belts run to a 5:1 tension ratio (although ratios as low as 10:1 run fine without slippage).
View attachment 4209485
Here is a typical drive with 5:1 tension ratio at full load. Wonderful. Look what happens to tensions when the loading is lightened or the drive stops:
View attachment 4209531
Now add a backside sprung idler tensioned for full load.
View attachment 4209532
Same result right? Now analyze at low or no load:
View attachment 4209533
Huge difference... belt tension lowered by 1/3!
If a drive only see's constant loading (air compressor for example) a sprung idler doesn't offer much advantage. If a drive will see variable loading (like mowers).... a sprung idler lowers tensions considerably and increases life on belts, sheaves, and bearings. Adds cost though. Hope this helps!