SIP, H323, PRI, BRI etc all support separating call signaling from the call audio. That makes it very very easy for engineers.
With analog, the tones are mixed in with the speech and at the same frequencies as human speech (historically it had to be done that way in order to survive transmission across all the analog PSTN network equipment of the early 1960s).
For mobile call control and similar features to work with analog, the IP Office would have to remain listening in to the call all the time, and be able to accurately and reliable pick out tones from all the other noise that is happening. I suspect it could be made to work - but only at the cost of a lot of additional components and processing power that the market wouldn't have accepted.
Voicemail also has to do the listening for DTMF tones trick, but does it with the help of a full PC processor, and still gets false positives from those people whose speech can match DTMF tones.
(the IP Office team could maybe have done something with passing analog calls through the voicemail server to do the tone detection and then tell the IP Office what digits had been pressed)
With the current kit I don't think it could be done, the IP Office code probably has a simple "analog trunk = no call control" logic switch. You would have to route your analog line to something like a SIP ATA that can do mid-call tone detection, if you can find one, and it doesn't result in too many false detections - and eventually you'd reach the point where it would be easier just to switch using full SIP trunks.
[I am older than public DTMF - that is slightly depressing]
Stuck in a never ending cycle of file copying.