How to understand why casting directors don't respond to letters or emails
The basic answer to this is quite simple - most casting directors (as well as most directors, agents, producers etc.) get so many letters and emails it is not physically possible for them to respond to every single one.
Although responding to mail is a part of their job, their primary task is to make sure that the production they are casting for has all the roles filled as quickly and efficiently as possible. The task of identifying and auditioning relevant people for a particular production can be a huge one, even when the cast is relatively small. People can get literally hundreds, even thousands, of applications for just 3 or 4 parts. It can take several days just to read through all the CVs and 3 or 4 roles can take several weeks to audition for. When you're talking about mid to large-scale productions casting can very easily take months, even with the casting director(s) working full time.
It is also important to recognise that a casting director needs to be going to see productions and showcases on a regular basis. This is very time consuming but vital if they are going to find new talent for their productions. In comparison, answering an email that says 'I am writing to introduce myself…' is not. Once you have sent the letter/email they have your information. Every casting director and department will have a way of storing the information of people they think they may use at some stage. Whilst it would be great if they let you know that they have received and are considering what you've sent them it's not necessary that they do where other parts of their job are.
It is the job of a casting director to look at as many actors as possible and the vast majority put a lot of time and effort into communicating and interacting with performers as best as they can. It is not a slight or ignorance that stops them sending a reply, it's practicality.