If the message said ‘Install our lovely new firmware and your printer will print three times faster, use half the ink and energy to produce perfect pictures every time’ then install away, however my experience is that the message just says ‘new firmware available – update?
Over the past 25 years of inkjet printers the technology has changed significantly, and during that time the OEM’s have spent a fortune on legal battles with the third party manufacturers protecting their IP (Intellectual Property) rights.
At the same time, they have earned themselves a reputation as ‘Rip-Off’ merchants, selling cheap printers and making money on expensive consumables.
When it comes to firmware, updating to the latest version can sometimes make things worse.
This is most common in the printer industry, where firmware is used to limit the use of third party ink cartridges.