You definitely can "win" (beat regular 9 floors) with more than just cleavers or bow. In fact thats what I was doing most of the time, and usually breakpoint was Magma Core+ (F16-18) for most of the setups. Yes you can get unlucky with either drops or the enemies / events, but thats how the game work.
Regarding poison and burn, I agree. Poison is simply cannot be survived after regular floors anymore, burn can be mitigated by block but on high values you also start having problems (like you cannot build more than 999 block for some reason and will die eventually).