No, a lot of our house rules are a bit arbitrary; only created when we personally run afoul of an irksome turn of the rules.
I'm saying that I don't agree that using strength for intimidate is a logical rule (within the context of debate, as all house rules are reasonable in the context of a DMs game). A high strength is one tool that a person can be intimidated with, but it, in and of itself, does not make a person better at intimidation. No matter how many ripply muscles you have, they don't make a difference unless you know how to manipulate a subject into fear of them. Some characters have a high strength, but aren't very big, while others have swollen body builder muscles without having a lot of strength. Height can also be intimidating, but a person 6'6" doesn't get a bigger bonus than someone 5'5" when intimidating someone. It's all about how you use your assets to instill fear in someone which is a combination of learned skill (ranks and/or feats) and natural ability to influence others socially (charisma).
Edit: in other words, strength might add an equipment bonus as the tool used with a skill, but not as the ability associated with the skill.