While there are army builds that get around the use of vehicles for every army, it takes away a lot of the game. An army like DE would be nerfed as they don't have armor and rely pretty much on maneuverability and speed. IG get nerfed as well as that's where they draw pretty much all their heavy hitters from. Again, this doesn't necessarily mean there aren't ways around not using vehicles. Though, I have to wonder where the line is drawn. Do you allow walkers too? Why stop at jetbikes/bikes? Are skimmers allowed then? It's an interesting concept, just have to be careful of where you draw the line. I think if you ran a tournament like this, I would put my money on a nids army winning.
"There is a cancer eating at the Imperium. With each decade it advances deeper, leaving drained, dead worlds in its wake. This horror, this abomination, has though and purpose which functions on an unimaginable, galactic scale and all we can do is try to stop the swarms of bio-engineered monsters it unleashes upon us by instinct. We have given the horror a name to salve our fears; we call it the Tyranid race, but if it is aware of us at all, it must know us only as Prey."