I think that's lazy analysis.They're aiming for a level of Clean'N'Safe™ just above Happy Days. That means no veneral disease, urinary tract infections or characters discovering dangerous opiates.
"The Goes Wrong Show", or "Arrested Development", are proof that you can have extraordinarily dense and well-crafted comedy without "veneral disease, urinary tract infections or characters discovering dangerous opiates". But like everything in life, achieving perfection is extraordinarily difficult, requiring both inhuman levels of effort AND a strange unpredictable confluence of luck.
If anything, I'd guess the primary issue is not "what are we allowed to say on TV", it's the way the scheduling is structured, the extent to which the primary writers are able to construct the entire structure (over many episodes) in their heads, and then have time to polish every detail of every episode. That's a rare thing; and it's a lot harder to approach perfection when you're rushing to finish an episode over the next two days, and have no idea how you plan to tie together all these various plot lines by season's end in seven episodes.