I suspect it was just the practicalities. And the fact that both George and Frederick had a great horror of being thought ridiculous or laughed at .
The Dss. of York only died in 1820. Conventions of the day required a seemly interval before marriage - not a precisely fixed term, but probably a couple years ( mourning itself was at least a year) . By then the Duke would have been 60. Not definitely too old to sire a child, but the likelihood would be fast diminishing. And by 1825 he was suffering from the heart failure that killed him in 1827. Not a very big window.
Also, though the idea seems ASB when applied to one of his family, he really didn't seem all that interested in sex. If he had remarried I'm sure it would have been a "it's your duty" thing. Add all that to the difficulty of finding a princess or widow young enough to have children ( preferably without any already) , and the Duke's fear of people mocking an old man marrying a girl young enough to be his daughter.
George, similar, though less so. He had few more years, but on the other hand, he was decidedly more unattractive personally than Frederick. And a lot more vain and sensitive . I believe that George did instruct his ambassadors to quietly put out feelers to see if a suitable prospect could be found, but they were discouraging.
Still all said and done both Edward and William managed. So it could have been done.
So for both brothers it was almost a question of vanity. Well if one or both were to remarry, who would be considered candidates for royal wives? And, second, sense a Regency would no doubt be necessary, who would serve as Regent? The Widow or a Royal brother, like the Duke of Clarence?