I know that Hamel bases have a couple of defects for the purposes of doing analysis in infinite dimensions:  

(1) Every Hamel basis of a complete normed space must be uncountable.

(2) For every Hamel basis of a complete normed space, all but finitely many of the coordinate functionals are discontinuous.

I also know both (1) and (2) are false if completeness is dropped.

Here are my questions, which I have labeled A,B,C,D: 

A. I don't see why (1) is a serious problem. An uncountable Hamel basis seems just as hard (or just as easy) to work with as a countable Hamel basis. After all, Hamel bases are about unique representation as _finite_ linear combinations. What am I missing?  

B. (2) seems like it could be inconvenient. But I don't have a concrete understanding of why. What does (2) stop you from doing? I see that it means the standard dual basis for the algebraic dual is not basis a for the continuous dual.

C. Is there something else that goes wrong with Hamel basis in infinite dimensional spaces? Something, perhaps, that is more obviously inconvenient?

D. Is there something that goes wrong with Hamel basis in *incomplete* infinite dimensional spaces? 

**Edit:** Some commentators have pointed out that Hamel bases cannot be produced explicitly for the most important spaces. I was aware of that, and should have said so. Is there anything else for C, other than (1),(2), and the lack of explicitness?