Does 慢一点 mean "be careful" even in a general context?
I don't think that 慢一点 is the same as 小心一点. 

I am from Manchuria, and as far as I know, sometimes when people are gonna leave each other, a person may say 慢走 or 慢点走 as an expression for "Goodbye". Maybe a personal bias, I don't think 慢走 is frequently used. 

I also agree with you that, doing things slowly may not always help.