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).
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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:
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Now add a backside sprung idler tensioned for full load.
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Same result right?  Now analyze at low or no load:
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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!