Of course. That's why I use the Alternate Ability Score variant in the first place... so that I can flex how/why a check is to be made. I'll sometimes use CHA (Persuasion) for intimidation checks too, depending on who is doing it and how. My original post was to highlight a way you can remove Intimidation as a skill and still have things run fine.
I use the alternate system as well (loved since the next playtest), but my point was also that Intimidation and Persuasion are not the same thing. Intimidation could be a type of Persuasion I guess, but obviously not all Persuasion is intimidation. If you intimidate someone - they know it. If you persuade someone, they might not even realize it.
So, in my games you could have:
STR (Intimidation) or CHA (Intimidation) or possibly even INT (Intimidation), and..
CHA (Persuasion) or Wis (Persuasion) or INT (Persuasion)
To me: CHA (Intimidation) and CHA (Persuasion) are not the same thing and have different affects on the roleplay. So even if you are using CHA to intimidate, the person knows they are being intimidate, ie. threatened in some way. While CHA (Persuasion) could be a bribe, or clever word play, but it wouldn't be a threat. How someone reacts to being intimidated or persuaded are different IMO.
Now, I do think Athletics and Acrobatics could be combined into just Athletics and then you chose which attribute to use STR or DEX for the check. Though I do see some value into providing the extra granularity to describe different types of athletic training.