Exactly. 5E was clearly designed around the RAW simple initiative system. Creating a new initiative system that adds extra costs for using certain types of actions vs. others is pretty much guaranteed to cause imbalances. It would be like suddenly changing football by saying incomplete passes cost the passing team 5 yards of field position. Suddenly passing is higher risk than before.
As I've learned to my chagrin, using analogies on this forum risks a deluge of literalism: we could enumerate countless reasons why this initiative system is not
like adding a 5 yard penalty to incomplete passes.
But I'll acknowledge your intent, and agree that changing the rules changes the incentives. But I have to wonder if the game is so well balanced in that regard that we shouldn't mess with it, or do we simply accept current imbalances as "the way the game is"? I believe the latter, and my point was that if we had been using Greyhawk initiative all this time we would have simply accepted a different set of imbalances as the default state.
And, sure, you can pick any one imbalance...such as the additional penalty to TWF...and say "see how terrible this idea is", but that's an implementation detail that can be addressed.
In fact, one thing this new system offers is a way of addressing current imbalances. Is there already too much incentive to use ranged instead of melee? Great, increase the die to d6. TWF unfairly penalized? Roll once for each attack and take the lower. (Yes, that raises additional questions...instead of whinging about it think up solutions!)
Maybe this gets too complicated, but I for one think it's worth examining the options and looking for design solutions rather than just pointing out the flaws and dismissing the whole idea. The current initiative system has so many flaws of its own that it's worth considering.