You've nerfed or buffed supposed skill classes depending on DM adjudication.How? How would any of it break? 'instead of using Cha for Intimidation, you can use Str' just replaces all references to Cha with Str. NOTHING HAS CHANGED besides there being more room for character concepts to actually do stuff you'd expect them to be able to do.
If a PC can simple swap Strength to Intimidation, what's to stop a cleric from using Wisdom for EVERY skill check by praying first.
"I pray for guidance and recall a holy story related to this situation) ".
Or a wizard or any intelligence class adding bits of academia into everything to roll Intelligence.
It works as a one off. It doesn't upscale. That's why it is done or suggest as a class feature (Holy order, Primal Knowledge) to limit use.
And STR based Intimidation is cited so often as the only example that it proves my point that there just should 4-7 more skills to handle these situations. Perception and Investigation are separate skills. It isn't Perception (INT or WIS or CON) for a reason.