Roughly speaking, yep - Common Crawl provides a sizable chunk of web data (420 TiB uncompressed, over 3 billion unique URLs, as of May 2022; historic statistics here[1]), and is updated on monthly basis. Not near-real-time, true, albeit relatively fresh.
A question to ask could be: how often do users care about information from a few minutes ago, compared to information that has been available for a longer duration of time?