My company spec is based in part around NACE MR 0175 and it calls out the maximum permitted hardness reading shall be 248Hv10 (237HB) for carbon steels although I believe NACE actually accepts up to 275Hv10 (sorry, not going to look it up for you, so just speaking from memory).
In very general terms, for NACE applications I've not seen minimum hardness being an issue or requirement.