Data and software tools were always "game drivers" in academia and industry. Nowadays, it's an almost priceless trend for the ones who are trying to be on the "edge" that most communities are open sourcing their results. And the other amazing part about open sourcing results is that datasets and software tools helped additional value creation are also published for free. And such a tendency is true and ongoing in various aspects (e.g. teaching, content, datasets, software tools, etc.).

However, as long and tools and datasets are getting more and more.

Technically spoken, integration of "custom" fields into BibTeX is already happening. For instance, very popular bibliography managers such as Mendeley and Zotero while exporting BibTeX-es in parallel embedding additional fields into exported file. Example of such field is "file" fields that helps aforementioned tools to maintain their libraries, it basically contains full (or relative) path to the scientific manuscript, which is usually pdf file.

And the very big question - should a community introduce additional optional fields within the BibTeX format in order to motivate people for creating publicly accessible datasets that could be easily cited in scientific manuscripts?

Nice description of the BibTeX format can be found here, here or here.