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within the term of the patent, the likelihood that anyone else independently invents the same thing is sufficiently small //
The problem then is that there is little to no incentive for the applicant to share the idea. If it's something no one will come up with, then you can keep it secret and benefit from an indefinitely extended monopoly.
The quid pro quo of patents is early information about new inventions in exchange for limited time monopoly. Here you're encouraging inventors/companies to prefer industrial secrets.
If inventions meet your requirements but are kept secret then the public domain will be worse off as no one gets the benefit of being able to privately use/research the invention unless it can be replicated. With a patent the full details are disclosed.
Obviousness is very difficult to assess because some things that took many years developing are so ingenious that they seem obvious. The applicant always has the argument - if it were so obvious how come, in such a well worked field, with such demand for this invention, how come it wasn't already developed? The answer of course is that it wasn't "obvious" [to the skilled practitioner with knowledge of the prior art in the relevant domain].