Why aren't there framing issues? Framing is nothing more than determining when one symbol stops and another symbol starts. So with DTMF you have to end one tone pair and begin another tone pair is such a way that this transition can be reliably detected -- that's a framing issue.Thinking a bit sideways.....touch tone (DTMF) is audio, and therefore easy to record on an audio recorder. You'd probably only be able to realise a rate equivalent to about 200 baud , but it is a very robust data format, and no framing issues to worry about.....
Also, why wouldn't you be able to realize a rate much in excess of 200 baud? Even using the same tones as traditional phone DTMF you can probably get over 600 baud and since each tone pair conveys four bits of information, you can get over 2400 bps of data transfer. And there are many games you can play, particularly using high frequency tone sets, using larger tone sets, and broadcasting more than two tones simultaneously in order to increase both the baud rate and the data rate.