With a little practice, time invested is minimal, especially after first generation when all brood hens are trained. Most brood hens were offspring of previously trained hens so made effort much easier since mothers helped teach offspring we were not a threat. Every year we had to start with few first generation birds with walk reared pullets and those took more time like described above. My grandfather was all about easily handled birds and so it was worth effort on front side with hens to have them as tame, especially with brood hens that may be expected to give several years worth of service. Getting flogged by hens is only part of problem, they also put their chicks at risk trying to flog you the keeper. Overall flogging is not all that painful but does get aggravating when you are pressed for time or simply wanting to have a pleasant day.
In one flock co-existence is a negative once more than one is fully mature. The game roosters will eventually fight of rights to harem. With a mixed breed setup, even that is dicey. A young game will eventually challenge the old non-game and either be killed himself or run the non-game off. I tried recently (again thinking I figured something out) to keep a gamecock with American Dominique stags where once the dominique stags would try to stand their ground even briefly, the game would whip them then run them almost to death and would kill them if I or dog did not intervene. The game has much more stamina and no interest in relenting so long as target will not leave his territory.
Using games in dual purpose capacity is doable when only one mature rooster kept. You can also keep more than one on one barnyard area so long as they have discrete flocks and territories do not overlap. Separation of territories is difficult for most folks to realize unless you have several outbuildings serving as roosts / loafing areas and multiple fences that can serve as easily recognized territory boundaries. We had a couple walks were the two rooster system worked well. Common denominator in addition to larger more complex barnyard area was full time farmer managing grain-fed livestock in multiple feed-lots. Lots of oversight is required and we never allowed situation to persist more than about 6 months of the year.
We did realize the dual purpose with my grandmother's flock over several years where a gamecock and two hens free-ranged with about 30 Plymouth Rock and Road Island hens. Rooster tried to cover all hens but owing to realized roosting setup, gamehens were preferentially covered / mated ensuring good fertility of eggs. Hybrids that did manage to hatch despite effort to collect all eggs were easily distinguishable based on genetic markers. Size was a dead giveaway but color and feather development were more than adequate to distinguish.
