After sending ping on the email I immediately got such answer:

"""

An HBA firmware image is made up of firmware and nvdata. It is very likely the firmware will be the same for all boards from different vendors unless they are on a special firmare stream. However, the nvdata can and usually is different between vendors. The nvdata is where they can add customizations for their specific systems and environments.

Each specific model has a specific nvdata which is why you see different binaries on our website. I recommend getting the specific firmware for each board from the vendor that built the controller. It is possible that some vendors could have the same name, but from what I have seen they seem to use slightly different names. I would not assume that two boards with the same name from two vendors are identical. If you are going to update firmware you should get the image from the vendor that built the board.

"""

Considering this, I don't think it is safe to add firmware from Supermicro for so generic name as LSI3008-IT.  Lets postpone this until we really have problems there.  Besides I simply have no source of images even for Supermicro.  ftp.supermicro.com where Austin sent me does not exist any more.

Nope.

 have they got back?

I've sent email to Broadcom to figure it out.

I was wrong, we do sell integrated integrated HBAs now in R-series.  I'll investigate the question of the firmware images.