Introduction
I'm going to go through the reasons as to why the specification as stated, cannot be implemented, and also as to why older technologies that may have allowed this implementation cannot be used.
Do note that even older technologies, would have required some sort of installation or agreement from the user- as a minimum 1 click.
Also note: It is possible to get files from a users system, but you still have to get their agreement through an action or prompt from their part!**
As to what you could do? Tukan already covers some nice alternatives but if I do think of something I will add it!
Basic Explanation
The most basic explanation is that this would be a giant unprecedented security hole. It would mean that browsers would allow a site to access files from a users computer hardware (DVD) without the permission of the user or the active actions of the user.
In your case you do have a valid non-malicious use for it. Imagine however all the malicious websites that would use this mechanism to steal stuff off the DVD/CD that is in the users tray. Imagine the privacy issues, security breaches, and even minor stuff like copyright issues.
Finally, and even worse, if the specific requested allowed access to the whole file system (including all drives like C:), a malicious site could steal everything on a user's system.
The positive (and negative for you) is that browsers have been incrementally locked down over the years and technologies/plugins/extensions/features have been incrementally either locked down, or deprecated/removed. Such technologies include: active X, java applets, and flash.
Finally, browsers like chrome and internet explorer themselves now'a'days run in sandboxes. See for example the article (and this is from 2013!!): Sandboxes Explained: How They’re Already Protecting You and How to Sandbox Any Program
They’re restricted to running in your browser and accessing a limited set of resources — they can’t view your webcam without permission or read your computer’s local files. If websites you visit weren’t sandboxed and isolated from the rest of your system, visiting a malicious website would be as bad as installing a virus.
Other programs on your computer are also sandboxed. For example,
Google Chrome and Internet Explorer both run in a sandbox themselves.
These browsers are programs running on your computer, but they don’t
have access to your entire computer. They run in a low-permission
mode. Even if the web page found a security vulnerability and managed
to take control of the browser, it would then have to escape the
browser’s sandbox to do real damage.
Active X (Deprecated) (Internet Explorer)
Let's start by saying that Active X would require the user to change their Internet Explorer Security Settings so we can strike it off immediately.
If a user did change their settings (see: Enable ActiveX controls in Internet Explorer ) and Enable for IE 11, a developer could use active x to access files on a users system.
Also note Active X is deprecated and rumour has it that it may not be around for long.
Java Signed Applets
Java Signed Applets could access the local file system.
However, Applets are no longer supported in firefox and chrome. They do run in Internet Explorer though IE is deprecated as well (since people are moving to Edge).
There's a very well written answer on the topic here: How do I run Java applets? [duplicate] and Why is the Java plugin (JRE) disabled in Chrome?
Adobe Flash (Previously Macromedia)
First off, flash has been removed from most Internet Browsers and is officially considered dead. Additionally, after Flash Player 10 it was possible to load a file but the user had to select it himself through a dialog (see: Can Flash action script read and write local file system? ).
FileSystem and FileWriter APIs
You can read and write using this API. However, it again requires the user to interact with the webpage and to select the files themselves.
References
