Hmm yeah, the Wikipedia article about the Smartmodem mentions that problem. “However, while the 25-pin connector on the modem side had more than enough pins for this purpose (even some meant for this purpose), the computer side often had far fewer pins connected and controllable, if it even used a full 25-pin connector at all.”
Using a single-byte control code to switch modes would only work if one of the following is true:
1. The only thing being transmitted is uncompressed text.
2. There is a software layer between the application and the modem, which inserts the aforementioned ATY sequence whenever the application sends the mode-switching byte.
3. The application speaks a protocol like PPP that can avoid ever transmitting the mode-switching byte.
Sadly, although PPP would have been able to avoid sending a DLE just fine, it *cannot* avoid sending the Hayes +++ sequence.
That is, it can avoid sending any byte you want, substituting any instance of such bytes with a sequence of other bytes…except 5E or 20 through 3F.
+ is 2B. 
But wait, if Hayes had gone with the aforementioned DLE/ATY scheme, then wouldn't file transfer programs and the like have known to insert the ATY sequence after every DLE? Only dumb terminal programs wouldn't, and there's no keyboard key that sends a DLE.