What is the problem with adjusting brake levers to end their travel "too close" to the handlebars?
The issue with having brake levers which have travel that ends very close to the bars is that, as the brake pads wear down, the brake levers will hit the handlebars before the brakes are fully engaged.

This can be mitigated by regularly inspecting your brake pads and adjusting the brakes to compensate for normal pad wear. You could have them that close if you stayed on top of the adjustment demands, but since the average rider does not adjust their brakes this frequently or pay as close attention to this, common advice is to avoid having the levers too close to the bar.