My owners manuals have all stated to run the engine at WOT when mowing or blowing snow etc. No, you don't need WOT for tooling from one place to another or for going from front to back yard, nor even for towing a trailer around your property etc., but that is not what we are talking about here as far as running your engine at WOT while mowing. Running them below WOT under light cutting conditions will not harm anything on the engine really, but it just might cause more harm than good for your hydros which are designed to be cooled most efficiently by their fans with the at WOT.
When I say my pwners manuals, I am talking all the way back as far as 1969 manuals for JD and Jacobsen garden tractors that utilized single cylinder Kohler/Tecumseh/Wisconsin engines, which were very basic in design compared to today's engines.