I founded approximatelabs to essentially chase this out and show how much rich fruit there is in this space. See approximatelabs.com
It is not traditional ML to me, which has a "row-wise" way of thinking. Instead, we are thinking columnar-ly (like you would if you were an analyst), and representing entities and attributes as tokens (not individual features). To me, describing "data" requires creating tokens that represent the information of the whole of the data. There are a few different ways of approaching this, but technically, the way we are approaching this is representing columns via aggregations (both exact and approximate (sketching algorithms like HLL, TDigest, etc.)). These columns now have representations that can be worked with by transformers in the same way they look at "tokens" of language, now we have "tokens of data" (also think multi-modal patch embeddings with images, but with columns of your data).
To power this, we actively are scraping "all of the data" as you say, and have over 100M tables in our store, and hopefully will push this to over 1B in the next week or so (about to run our next big parse job). We plan to open this dataset to public / research very soon, so looking forward to that. Shortly after that we plan to publish some papers about the actual details of our multi-modal tabular-data foundation models and techniques we have tried and learned from!
Towards the last part of your question: what use case would this model open up? We believe that the entire data stack (currently modern data stack) is about to get a revolution in the way that LLMs caused "symbolic" language models to get revolutionized. Think catalogs that are actually smart and semantic (not just based on the semantics of the metadata, but also of understanding natively the content of the data), observability that is in embedding space and is able to self-explain deviations, and most importantly: accessibility. Since LLMs have proven that they can lower the accessibility barrier to technical concepts, we are expecting and planning on our product being "the new excel", where everyday people can actually leverage the analytic power of things like pandas and sql to answer their questions and trust the results. Heavy bias, but I think the space is about to get very, very hot, and early competitors are starting to pop-up around the chat-bot use-case, and we believe we have a huge edge because we're making our own models + starting at the fundamentals.
Happy to answer any other questions too!