Let's consider my class implements Default. Should I make new() function?
Yes, if that's a common and useful way to use your type. Convention is to have a new method (with or without parameters).
If there is no single dominant way to create the type, maybe only specific named construction static methods is better.
I implement Default, which delegates to new(). I think that new() is extra.
It's your choice, but it's not uncommon to have new even if you implement Default.
Unless your type is zero-sized, there's probably some setters that your users are going to want to call right after creating it. Make those arguments to new.
There is no setters, which can be placed into new.