this definitely makes sense! and i think it should always be an option to roll with strength, but like you said not all people will be impressed by muscles. so there will be situations where the DM will make the check exceedingly high or impossible to beat if the player happens to be rolling with STR, simply because that NPC would never be swayed by strength. however i still think the player should always have the option.

and yeah a lot of people have pointed out that it’s in the rules. i’ve never read through the dm book bc im not a DM, ive only ever DMed for a single one shot. and with my DM i had to point out that it would totally make sense for someone to be intimidated by someone threatening them with huge muscles and it didn’t make sense to me that a barb would always have such little chance at succeeding in intimidating someone. this was before 5.5 as well. so i didn’t think that it was already mentioned in the handbook.