To Be (potty trained) or Not To Be (potty trained)

For those of you changing toddlers diapers...
As crappy as it to change diapers let me just give you a few things to think about to maybe, possibly, help the chore not seem quite as bad.
My little Liza was recently potty trained pretty much on accident around the time she turned two. I really wasn't ready for what came with it, though. I don't want to seem like I'm complaining but I just wanted to let you know potty training early isn't all good.
Here are the pros of early potty training for us. 1-The actual headache of potty training is behind us. 2-I don't need to use huge amounts of diapers anymore (she still wears one at night) 3-No more toting stinky diapers to the outside garbage.
But...here are the cons. 1-Eliza now wakes up at all hours of the night to use the "toywet". 11:00pm, 2:30am, 5:00am. Sigh. She has a diaper on but wants to go on the toilet. I think she is pretty young to hold it all night. Maybe soon? Please? 2-Pretty much every place we go we have to use the bathroom. I'm not a huge fan of public bathrooms so I don't love this much. Especially with pudgy fingers trying to TOUCH everything in the stall. 3-She needs to use the toilet ALL the time! Mostly at the worst time-something is boiling on the stove, I'm in the shower, we're in the car, etc. And you can't just have her wait a few minutes until its more convenient. When she says she needs to go she needs to GO. 4-I am not off poop patrol yet. I still have to go to the bathroom with her and pretty much help her every step of the way, which, unfortunately includes wiping poop...still.
So there you have it. Pros and Cons of early potty training. Did I leave any out? What do you think? Better to potty train ASAP or wait until they are a bit older?