I'd like to hear your input on this matter.
I'm really unsure whether the above sentence makes sense. If not, what is the correct version of the sentence; and if it does make sense, are there any other formats of the same sentence? (I'm really keen on keeping the word "input" in the sentence, instead of using the word "thoughts")
You ask if the sentence could be formatted differently. It could be made more concise by saying:
I'd like your input on this matter.
There is no need to say "to hear". If you are in a face-to-face conversation, that's implicitly obvious, and if you are communicating via email, then you may not want to "hear" the input (you may want to read it instead).
As for your primary question, "input" is fine there. Wordnik has this definition:
input (noun) Contribution of information or a comment or viewpoint.
and I would say that this usage is more common than obscure jargon. For example, one blogger's post begins by saying:
You may think your kids are “too young” to offer input on vacation plans or suggest workable solutions to a problem that’s stymied you.
I hear this exact sentence or similar uses of "input" pretty much every day. I work in software development in a US corporate environment. In that setting, asking for "input" is by far the most common way to express this concept. Asking for "thoughts" is significantly less common, and asking for "contributions to a debate" is quite rare.
In my view, the is a slight difference of meaning: "Input" is something expected to form part of the final result, while "thoughts" or "contributions" carry no such implication. Of course, that expectation may be frustrated.
Obviously this is a fairly recent coinage, derived from "input" in a more concrete sense, and quite likely specifically in the sense used in computing, or at least strengthened by the frequent use of "input" to describe what is provided to a computer program. But that is how language changes.
