Yes, civil engineers commonly go for PE licensing for this reason (signing off on designs of things used by the general public), and PE licensing requires or is greatly helped by having an ABET-accredited degree. Sometimes, other engineers get PE licensing if their line of work needs it. In addition, an ABET-accredited degree is helpful with the patent exam prerequisites.
Otherwise, ABET accreditation is typically expected in more traditional engineering areas (e.g. chemical, electrical, industrial, materials, mechanical, nuclear) as an indicator of quality for programs at schools that do not themselves have top-end reputations in the fields. Hence, new programs in those areas will typically seek ABET accreditation. However, new programs in less traditional fields are less likely to do so, although BC seems to be interested in seeking it (however, ABET accreditation cannot occur before some students in the program graduate, although if it is granted, it is retroactive to those students).