"The Big Sisters [are] almost impossible to beat without dying."
The tradeoff with difficulty in any game is that if it does NOT seem overly tough on the first playthrough, it will seem too easy on subsequent playthroughs. BioShock 1 is waaaay too easy on replays, even on Hard. After a couple of playthroughs of B2, you'll probably never get killed by a Big Sister again. In fact, while replays are not quite as easy as B1, they are pretty dang easy. The variety of choices you can make in the game is primarily what makes B2 replays still fun.
"a) the drill dash is not available until later on in the game, and this move is often crucial for survival..."
My first playthrough, I don't think I ever used the Drill/Daddy Dash, so it can't be crucial for survival. My third playthrough, I used nothing but the Drill and plasmids for the entire game. It made the game more interesting, but obviously still survivable.
"(b) unlike the wrench, [the drill] requires 'ammunition', which is often scarce to come by, especially on higher difficulty levels."
The wrench is a melee weapon, period. The drill can also be used as a melee weapon, so as such it does not "require" ammunition. With fuel, the drill is no longer comparable to the wrench. It is a whole other weapon. I had to laugh when I saw that drill fuel is scarce. My first playthrough I rarely used the drill and it seems drill fuel is all the ammo I would run across.
"You are pretty much guaranteed to drain the drill's ammo in any serious fight;"
In my drill-only playthrough, from beginning to end I was able to kill Big Daddies just by turning on the drill and moving into them (a Daddy Dash is actually counter-productive). It is ridiculous how easy that is. For killing BDs, the drill, upgraded as you go, is better than any other weapon. Even when playing with all weapons, I *always* use the drill on BDs. No elaborate planning or set-up is required. See one, kill it. Easy. Oh, yeah -- and there was ALWAYS plenty of fuel around. In addition to what can be found, I had plenty of money for drill fuel because I didn't need any other ammo. And if you run out of fuel while killing a BD, you can freeze him with an Electro Bolt and whack him with the drill until you finish him.
* I should have noted that I always make the Drill my first two upgrades at the "Power To The People" machines, plus I make sure to get the Drill tonics as soon as I can.