I can't get one thing straight. The RFC 2616 in 4.4.5 states that Message Length can be determined "By the server closing the connection.".
This implies, that it is valid for a server to respond (e.g. returning a large image) with a response, that has no Content-Length in the header, but the client is supposed to keep fetching till the connection is closed and then assume all data has been downloaded.
But how is a client to know for sure that the connection was closed intentionally by the server? A server app could have crashed in the middle of sending the data and the server's OS would most likely send FIN packet to gracefully close the TCP connection with the client.
You are absolutely right, that mechanism is totally unreliable. This is covered in RFC 7230:
Since there is no way to distinguish a successfully completed, close-delimited message from a partially received message interrupted by network failure, a server SHOULD generate encoding or length-delimited messages whenever possible. The close-delimiting feature exists primarily for backwards compatibility with HTTP/1.0.
Fortunately most of HTTP traffic today are HTTP/1.1, with Content-Length or "Transfer-Encoding" to explicitly define the end of message.
The lesson is that, a message must have it own way of termination; we cannot repurpose the underlying transport layer's EOF as the message's EOF.
On that note, a (well-formed) html document, or a .gif, .avi etc, does define its own termination; we will know if we received an incomplete document. Therefore it is not so much of a problem to transmit it over HTTP/1.0 without Content-Length.
However, for plain text document, javascript, css etc. EOF is used to marked the end of the document, therefore it's problematic over HTTP/1.0.