Running on muffs does not give the exhaust back pressure it sees when the engine is in the water, so what seems like the perfect set- up on muffs might not even start when in the water.
The fact it idles means there is enough fuel getitng in to keep it going under next to no load. Somewhere between 1200 & 2000 rpm (depends on the engine) the fuelling moves form the idle jets to the main jet, so once you get it going it will (should!) happily run. This is what you are experiencing.
If the idle is is set a touch on the lean side, when you open the throttle the lean mix isn't quite enough to keep it going, as the acceleration puts a fair load on the engine.
If you imagine the fuel going in releases a certain amount of energy, which at idle has to overcome three main things: 1) the exhaust back pressure 2) bearing & piston ring friction & 3) compressing at least one other cyl in time for the next "bang".
So, as you accelerate, these three don't go away, but added to the pile of energy consumption is the power needed to spin the prop & accelerate the boat. If you are running slightly lean, the carb can't predict what you are about to do (i.e. open the throttle) & react fast enough, and so the "spare" energy to push the boat along from the lean mix is not enough to overcome the extra power demands, so it stalls.
Ironically the bit where the idle jet can't let enough through is a tiny proportion of the operating regime, hence by richening the mix and yes, your idle becomes a bit less eficient, but at least when you open the throttle, enough petrol can be dragged through the crab to allow the engine to spin faster & let the main jet take over.
The reason I am pretty certain?
I've had it happen to me on three engines, most recent time when I upped the pitch of my prop & the "ideal" idle mix settig for the old prop wasn't enough to get the bigger pitch prop (& therefore load) prop past that crucial point.
+1 for Uncle Al's comments.