They don't have radio lines because RTS games don't really work that way.
That may be true of current RTS offerings, but given we're talking purely theoretically at the moment it might be an interesting thought experiment to consider:What would an RTS be like if they did work that way?
(that is, featuring lines of communication).
I think the player would have less direct control over individual units: instead of giving very specific instructions on movement, placement and activity of units (move here, shoot that, deploy this), the player would give more general instructions (hold this area, engage this target) which the units would then go about doing in a more autonomous fashion.
Rather than individual units (1 infantryman, 1 rocket soldier, etc.) you would probably command small quads composed of those different individual parts. You would give the squad their objectives, but it would largely be up to their command AI as to how they achieved it. For example, you might order a squad to defend a group of buildings, but it would be up to the AI to decide to put a sniper on the roof (or not).
If a line of communication was cut, you would be unable to send or receive information from a squad -- they would probably be hidden by fog-of-war, and would continue to act autonomously based on whatever orders you had already issued until communication was restored. If all objectives were achieved they may simply hold their position, or they might try to restore communication for themselves. Perhaps you could influence this behaviour by setting priorities.
Obviously, all of this would rely on more sophisticated AI than is often present. Individual units would still operate in much the same way as usual, but rather than receiving orders from the player they would receive orders from the AI for their squad, which would be trying to achieve the objectives set by the player.
Depending on the type of the lines of communication you might have a delayed flow of information. Perhaps a radio line allows you to immediately change a squads objectives and see immediate progress updates, but if the radio is down (jammed, dead operator, transmitter destroyed, whatever) you might have the alternative of sending runners back and forth with orders. Your units would not be fully lost in fog-of-war, but you would get "snapshot" updates a minute or two after events actually transpired. You could issue a new objective, but it wouldn't reach the squad immediately, and they would continue to act on the previous objective until it arrived. Imagine the tension of realising you need to preserve a bridge you had previously ordered destroyed, but not knowing if the new orders would arrive before the squad blew it up.
As noted above, this would probably appeal to a smaller niche of players, as many are used to and expect the more direct control that existing titles give them. That niche may or may not be worth pursuing.
In a discussion of different game play styles, you should never feel restricted by the styles of existing games. You might find some fantastic and different ideas by considering something completely different, and you'll probably find some terrible ideas as well (and perhaps gain a better understanding of why existing games are the way they are) -- you'll probably get a lot of "ok" ideas that aren't terrible but need more work, or which are fantastic in theory but may be tricky to implement; if you can make them work, you might just have a new sub-genre or genre on your hands!