The fighters at the time couldn't hang with the bombers, so the battle of attrition would only be over easily fixed airfields. No strategic targets would be struck as the bombers get shredded over the home fields of the fighters. The Allied bomber assets would have been spent for no gain. That's where the attrition would have occurred. Bombing without meaningful targets.
Actually the building of the heavy bombers was a waste.
As the above link shows (Air Force historian) the fighter-bomber was the ultimate effective tool.
The evidence was clearly in front of Allied Command, since they knew how well the Mosquito did.
Without dedicating resources to building heavy bombers, massive hordes of fighter-bombers and light, fast bombers could have been built and deployed.