Although LHC experiments are toward the top of the heap in terms of data rates, many particle and astronomical experiments produce "big data". One quarter of the DUNE experiment will acquire about 50 EB/year (that's exabyte), outputting about 10 PB/year to tape. LSST will produce data in the few PB/year range.
Not to belittle your examples, but in a historical context the LHC held a specific position. Remember that the ATLAS/CMS/ALICE/LHCb experiments started recording data at 10 GB/s back in 2008. Now, ten years later it is only natural that large data rates are becoming the norm.
