Wow, being a Mandarin native speaker, i’ve never thought about this question.
I’ve just checked the dictionary form Minster of Education. It doesn’t explain why we use it as a suffix. But some explainations may work.
zi, can mean little kids. the descent of some animals, refer to common people, etc. As a adjective, it describe some young, small, little things.
So, each term you guys mentioned are due to different reasons.
I think the dictionary can explain
haizi (child),
tuzi (rabbit),
pang4 ‘fat’ -> pang4zi
新娘子.
The following, I think is just because the pronouciation.
pan2zi (plate), panzi (plate)
bei1zi (cup)
zhuo1zi (table)
yi3zi (chair)
xie2zi (shoes) ,shiedzi (shoes),
wa4zi (socks)
chedzi (car),
But one thing is sometimes we can ignore the Zi when you say those words above in the middle of the sentence, especially you list some of them at the same time.
Like there are plates, cups, tables and chairs. You say Na4 li3 yo3 bei, Pan2,(always in this order, cups go first) zhuo, yi3. Unless you want to emphasise and pause after you say each item.
If you say I’ll drive (a car) to the school. The car is in the middle. So you say Wo3 Yao4 kai “Che” qu4 xue2 xiao. If you say Chezi in this case, sounds not that good to me.
Put it on the table. Fang4 Zai4 Zhuo(zi) Shang4. Usually we don’t add Zi. But in this case, if you do, sounds ok to me.
The following words, I think always go with Zi.
mao4zi (hat)
kuaizi (chopsticks),
bei4zi (blanket)
To Mother Theresa, there is no “wanzi (bowl)” at all
and all Zi here is not 3 tone, is light tone(i don’t know how to call it in English, somebody help me!)
Anyway, this is quite crazy, i think. 