That saying is definitely an "old" saying. Meaning back ~20 years ago when a 61" commercial ZTR was under $10k new and used ones in good shape could be had for $3k-$4k. And the other mowing options were riders. Either box store or something like x300 deere. Then yea.....it would cut mowing time in half. No only because of turns, but they could mow faster with good quality.
But now the market is flooded with ZTR mowers that are "homeowner" quality. Very small drive tires, ~5mph top speeds, Cheap feeling controls and feedback, crappy decks, not great cut quality, etc. So going from a GOOD rider to a cheap homeowner ZTR.....no....cutting mowing time in half dont hold true.
My FIL has a Bad-boy 26hp 61" cut. Supposed to compare to low-end commercial ZTR's. I have a 20year old scag wildcat. MUCH MUCH better quality.
I have a slight hill behind my 3-unit rental. His mower absolutely refuses to stick to that hill sideways. I have no issue whatsoever even in damp grass. Weight, balance, smaller tires, combination of all I dont know. And it tops out at 5mph whereas mine goes 10. He lives half a mile away so I ocassionaly have him mow and he just drives it up. So the painfully slow part sucks.
Regarding the standers....I personally hate them. They suck mowing under trees because standing on a mower you are taller than sitting on a rider. And you use your wrists to control, and no armrests. And yea, standing in general sucks.
My friend that owns a landscape business owns standers and riders. There are only TWO benefits to a stander as far as mowing and business is concerned.
1. They are cheaper
2. With employees....they are more likely to get off and move trash/debris rather than mow over or go around.