Image by NASA/JPL/MSSS
For Mars, my suggestion is that sediment transport by wind is aided and abetted by cold, relatively dense CO2 sublimating from the permafrost.
As with water on Earth, this would percolate through porous, unconsolidated aeolian sediments, producing or extending and clearing the outflow channels, chasms and canyons. Over impermeable bedrock it would flow on the surface, in time producing the intricate drainage networks seen in older terrain.
Sub-surface flow of some sort is clearly involved in the formation of Martian channels, as can be seen in the source area of Tiu Vallis. There, a large area of ground has collapsed upstream of one of the multiple heads of the channel, with an intervening area undisturbed (bottom centre, below).
The collapsed area downstream (centre) shows very large blocks to have subsided with their surfaces apparently intact, a further indication of sub-surface erosion and material loss there, rather than constant collapse of the exposed leading edge of the channel.
Channels without or with very few tributaries probably extend headwards in a direction exactly opposite that of the predominant net sub-surface gas flow, exactly as occurs with gullies or canyons draining near-surface groundwater flows in permeable ground on Earth. Both will cut back uphill overall, towards the source of the fluid.
Flows from the flanks will be far weaker than at the head, as the former have the entire length of the existing channel along which to emerge, in contrast to flows converging from an arc of 180 degrees on the limited expanse of the channel head. Hence these channels generate few tributaries.
The sudden emergence within the canyons of large channels from the edge of local areas of chaotic terrain has been attributed to the catastrophic emergence of groundwater under pressure.
The slow emergence of cold CO2 gas from the chaotic terrain, aided and abetted by katabatic airflow spilling down into the canyon over the surface would do just as well and seem a little less implausible. What mechanisms are supposed to have provided the pressure acting on the groundwater, constrained it successfully, and then suddenly released it?
The case I propose does not fit the currently accepted geochronology of Mars. However, the entire Martian chronological edifice rests on a comparison with the rate at which our moon copped hits from meteorites and collected craters.
Earth's moon is a gravitationally far smaller target than Mars, and if it has been orbiting Earth for a very long time, presumably Earth's far more attractive gravitational field saw to it that we got most of the incoming missiles.
Then, unlike our moon, Mars has an atmosphere and dust storms, which would bury many a crater, and clearly has. Half-obliterated ones litter the surface. If Mars had oceans, so would they and their attendant water flows, but that is the opposition's case, not mine, so I won't mention the possibility.
Also, the chronology proposed assumes a reasonably regular rate of impact of meteorites. One good asteroid shower any time in the last billion years would similarly tip the whole Martian chronological system into the wastepaper basket.