Here is the condensed version of the the response structure that I regularly use. You can read more about it at
www.daveandki.com, if you are interested. It is basically natural at the 2-level C-H-Pesque at the 3 level, and treats the 2C opener sort of like a 2NT opener at the 4-level.
after 2C [STR F2/2NT ART]
2D: Negative, can't promise 2 tricks, but see bust transfers
2M: Positive (2+ tricks), Natural, no worthwile second suit
2NT: Slam forcing (4+ tricks) any slam force that can't just bid the right contract
3C: Positive (2+ tricks), Catchall, Balanced or minor oriented
3D: Positive (2+ tricks), both majors
3M: Positive (2+ tricks), named suit and a minor
3NT: Positive (2+ tricks), three suits
4C: Your favorite Ace/keycard/Control count inquiry
4D/4H: Bust Transfer to the next suit. A hand that will likely be worthless unless played in the responder's long major.
After Opener's natural suit rebid, the cheapest suit rebid by responder is artificial and shows a balanced hand that might not take any tricks. The second cheapest suit rebid (below 3NT) is artificial and shows a trick and a misfit.
I usually like not to have anything much better than a king when I do a 4-level transfer. If your hand might actually be worth a trick in some other strain, you probably want to give a 2D response and then hope opener rebids 2NT so that you can transfer or bid your own suit naturally after opener's suit rebid.
So, in response to your original question, in the system that I play, you would bid 4H[TFR S] in response to a 2C opener. Are you going to be in 4S-1 on some hands where you could have been in 4C=, +130? Maybe. But, It is very difficult to stop in 4C after a 2C opener even when it is right. Also, opponents may well be able to play in 4H-1, +50/+100 or even in 4H=, -420/-620. Your transfer managed to get that alternative out of the box. It rarely pays to play 4C in any form of scoring especially when the potential for +420/+620 is so great. But, in many cases, when 5C or 3NT makes, 4S will also.
In the system that you have outlined, I am pretty sure that you are obligated to give a second negative (However you do that) to the 3C rebid. Are you going to play 5C-1 or 3NT-2 on some hands where 4S is cold? Yep! Probably more often than you would like to.
I am not a big fan of the "Dominating hand dominates and weak hand goes along for the ride" philosophy.