This is the best thing you can do to your bidding system. It is a method which is currently being played by several expert partnerships, and is highly recommended for anyone who is in a regular partnership with a good memory. However, it only works properly with a forcing or semi-forcing no-trump, so is not compatible with Acol.
One problem with natural responses is that you do not have a convenient way to show strong balanced hands. Traditionally you would start by bidding a minor suit. This is not ideal, because it means that the 2C or 2D responses do not promise a good suit. Some people use a 2NT response to show a game-forcing balanced hand. There are two reasons why I do not like this approach:
A much better solution is to include game-forcing balanced hands in the 2C response. When this is done we call it a relay. In its simplest form the 2C relay is game-forcing, and shows either a balanced hand or an unbalanced hand with primary clubs. Sorting out which type of hand responder has is very simple: after opener's rebid, responder usually has another relay available, which he uses on all balanced hands; so if he makes any other bid he is showing an unbalanced hand with clubs.
There are many possible systems of responses to 2C; it's almost certainly best to play an artificial method. It can even be turned into a complete relay system, where responder is able to find out opener's exact shape. Some notes for this method (which is highly complex and artificial) can be found here. An even more complex method, where the 2C bid also includes hands with diamonds, is described in my notes on artificial two-over-one.