The "usual caveats" about IGI are radically different from what they once were. The databases have been completely separated and are clearly identified as to their type. This means that unlike in the past where the "submitted by member of the church" records (aka sometimes no better than a random guess) were mixed in with the carefully transcribed records and so "IGI" search produced poor results, these days you get results from "proper" databases.
With the new search there are considerably more databases online than just the old IGI database. In fact the old IGI database is just a small part of the databases it searches. It is possible to specify a specific old databases to do an old style "IGI" search of just the transcribed records but I don't know why anyone would bother. So these days on the familysearch.org website its actually quite tricky to limit your searches to just the IGI database. As such its not really that relevant to call the familysearch website "the IGI".
So the only real caveats are about relying on a secondary source such as family search, however that caveat equally applies to FreeBMD, FreeReg etc which are also transcription sites, yet you don't hear people typically warning about caveats on that site, even though they should!