So my question is, how many people do you get to have in support before it is no longer solo diving? In ice diving, isn't the person tending the rope, just as much of a buddy as someone with you in the water? Perhaps more so, since they are there for your benefit only? (never ice dived and know little about it, so not sure of all the SOP, but I seem to recall the tended rope is standard every time)
There are divers who do ice just as caves or wrecks are done. They enter the water from shore or a hole and run a line from a spool. Swim out, swim back and so forth. This is very different than the typical class setting where the diver is in a dedicated harness and connected to a surface tender by a significant rope. In our class 3 divers went in at once and we were tethered together and a single rope went back.
In addition to the tender a safety diver was prepared to enter in short order. This diver has a somewhat longer rope so (s)he can sweep a wider radius and locate a diver that somehow got separated or incapacitated. One strategy if you become separated is to go up to the bottom of the ice where your air will last the longest and wait. By not wandering away the safety diver rope sweep will find you. As this thread demonstrates ice diving is done under many protocols with varying levels of safety.
As to your solo diving question no amount of surface support equates to a good buddy at your side if something really goes wrong. A minor entanglement could render the tender unable to pull you back. Ice diving is a technical endeavor and one would hope that a buddy has good situational awareness and skills. Such a diver should be a cut or 2 above the basic scatter brained insta-buddy.
Pete