I have absolutely no issues dropping the 'kids at the pool' when I feel the need to, public or not.
I don't have much issue with public honestly when are you going to see most people again you come across in public restroom, unless its your work or school. Even then its something we all do.
JUST POOP
Heres a tip if you need some ... flush regularly (to lessen the smell factor) and use air freshener liberally (if it’s available)
A survey that I found interesting a:

Do you ever poop in a public restroom

90% (284) Yes
9% (30) No (Leave)

314 voters have answered this question.

Under what circumstances does it take for you to poop in a public restroom

42% (132) Doesnt matter
25% (80) really have to poop
28% (89) on the verge of exploding
3% (10) NEVER

311 voters have answered this question.

If you do poop in a public restroom you will go if... (select all that apply)

48% (148) theres no one in there
24% (74) Another person is in there but using the urninal (Boys)
25% (77) Another Persons in there using the stall
28% (87) Another persons in there and you know they are pooping
59% (182) I go whenever

304 voters have answered this question.
When you poop do u make noises

38% (117) NO
58% (178) farting
17% (53) moaning
23% (71) grunting
3% (10) singing
12% (39) other

303 voters have answered this question.

If theres a person in the stall next to you and you fart what do they do

11% (34) Laugh
4% (12) Sound disgsted
15% (46) Fart back at you
80% (238) nothing

294 voters have answered this question.
Have you ever pooped in a public restroom and not flushed

52% (156) Yes
48% (144) No

300 voters have answered this question.

Why didnt u flush

25% (41) Forgot to... ooopps
23% (39) didnt like the place i was at
50% (83) wanted other people to see my work

163 voters have answered this question.

If there was a bathroom and the stalls have no doors, would you poop in it

34% (104) Yes
23% (69) No
7% (22) Yes if no one was in there
34% (103) Maybe depends how bad i have to go

298 voters have answered this question.

I for one refuse to poop in a public restroom. Home is really the only place I will go number 2. My reasoning is due to:

1. Most be clean (and given the responses to the survey you listed FullBlater, this doesn't seem very common)
2. I like privacy and taken my time
3. Making noises isn't cool.

At of all those questions in the survey the one that caught my eye the most is, 'Why didn't you flush?'

How the heck do you forget? Really, how hard is it to push the little handle down?

I would have to say that the home is preferable for the reasons that Drinking Theory has provided. However, there have been unfortunate moments where the ASU restrooms have been necessary... I mean common... I'm there like 10 hours a day... it's bound to happen eventually!

-SocraPees

I had to post that survey I truly don't understand how one forgets to flush ... how long are you in there were you aren't doing your business that you just forget you flushed already REALLY, you know what is sad the girls restroom women "forget" to flush their pee all the time can't tell ya how many times I have had to flush b4 going.

This is just plain amazing. I thought women were suppose to be cleaner then men!

This is like one of those SNL Weekend Update momements with the 'Come On, REALLY!'