Mavic has made some wheels like you describe, more or less. They're called "R-Sys" and they have aramid (Kevlar) spokes surrounded by carbon fiber sheaths. Here's an exploded view:
For more details about that, see the page the image is from: http://www.pardo.net/bike/pic/fail-001/FAIL-105.html
More seriously, yes, you could make wheels with "rope" spokes only. Why do the Mavic ones have the carbon sheaths then? I would speculate that the carbon acts as armor for the aramid fibers, which must never be nicked or they will fail. The carbon also stabilizes the whole arrangement, reducing lateral flex.
As for your notion that spoke tension would always be even if continuous fibers were used, I'm not so sure. The problem is that to achieve self-evening tension you would need to allow the fibers to run freely through some turning points. And if they run freely they will abrade rather quickly if they actually move at all. So you're at an impasse: either the fibers move and wear out prematurely (and perhaps lead to collapse of the wheel even sooner because of unstable geometry), or the fibers in fact do not move and you have the same tensioning concerns as with conventional wheels.
Finally, consider that spokes are thin and behave not like rods or struts so much as wire. So in a way we are already riding your wheels of the future today.