I just finished reading a book about Japanese grammar and there was a very enlightening discussion on the difference of は and が. I'm just a native user of Japanese trying to rediscover the language, so please don't take this answer as authoritative or formally correct. It's just my current understanding of the difference. Probably this isn't new to those who have been studying Japanese as a second-language, but being native I have never thought about the difference in a structured way.
Both は and が are used for subjects, but the main difference is that は indicates where the topic of the conversation is, while が simply indicates what subjects are for each clause that may exist in a more complicated sentence. That is why a sentence that contains more than one は sounds very awkward (the topic focus should be on one and only one item at a time), while a single は can be accompanied with multiple が in a single sentence.
From that view point, it seems the sentence
新しい合金が開発された。医療用や通信用など、用途は広い。
is most naturally rephrased as
新しく開発された合金の用途は、医療や通信など多岐に渡る。
I used a slightly different expression 多岐に渡る, which in this context means the same thing. To me, the key here is that the topic of this particular conversation lies in the wide variety of use, and not just the fact that the new alloy was developed. That makes sense given that the new development of alloy is exciting only because it has broad applications.
What makes slightly complicated is that the original phrasing sounds very natural when broken up into two like given. The development of alloy itself is a new piece of information, so it should be introduced in that way before leading to a sentence that conveys a more exiting piece of information which really is the topic of the conversation.
As for
象は鼻が長い。
the topic of the sentence is an elephant itself. Perhaps the conversation around this sentence is about elephants, and the fact that their nose is long is an additional piece of information that got into the conversation.
If instead you say
鼻は象が長い。
then the topic of the sentence shifts to nose. Perhaps the conversation was about nose of animals in general, and someone just mentioned the fact that elephants have a notably long nose compared to other animals.
On the other hand, both
象は鼻は長い and 象が鼻が長い。
sound very awkward to me, since the former is ambiguous as to where the topic lies, and the latter simply does not makes sense. Likely because 象が長い does not make sense by itself.