As a DM, the rules-as-written are more a suggestion than rules. As long as you’re consistent with applying your modified rules, give that Barb an Intimidation bonus based on STR or whatever you like. I have a pretty decent sized list of rules I treat differently than RAW, because some spells and abilities are never used - why cast anything else when you have access to Fireball?
You can always just ask the dm. Intimidate via strength for the barbarian isn’t all that uncommon
I am the dm, but yeah I get your point. There’s always ways to homebrew things.
As a DM, the rules-as-written are more a suggestion than rules. As long as you’re consistent with applying your modified rules, give that Barb an Intimidation bonus based on STR or whatever you like. I have a pretty decent sized list of rules I treat differently than RAW, because some spells and abilities are never used - why cast anything else when you have access to Fireball?