question about infill types

I find that 20% honeycomb works well for most applications. As you say rectilinear would be faster.
this page explains it quite well and has a lot of drawings of various infills and densities.

Tin

I've read the slic3r page but it doesn't go far than telling that certain types of infill might work better for certain models and denser infill is not required if the model doesn't have to be strong.
That's all it says.

Let's say for example you're printing a 5cmx5cmx5cm cube. Unless I choose to use 40% or so infill density, the top wall will have not enough support below it and the print will fail with top wall having holes.
I need something like Support, but for the inside of the model, if that makes sense.
Imagine this is a side cutout of a cube, terrible illustrations but I think you'll get the idea:

At high infill, it will print fine, but with wasted filament, print time, and strength and weight I don't need.

At lower infill, the filament of the top layer will not have enough support below it and I will end up with holes on the top of the cube:

I'm guessing something like this would help and also not waste as much print time and filament:

Basically something like Support but for the "inside" of the model.

I hope I could explain.
I can't find such 3d infill type or anything else that will help and I won't need to print almost everything at 40% infill.

I printed the bridge test print. Seems like slow is better. I dropped the bridge print speed to 10 and pretty much eliminated fill by adding perimeters. the first test print not very successful dropped some layers on the first level. and level 4 a mess stopped the print . the second attempt looks very good.  some bottom layer sag. the point is with the right settings you should be able to bridge 50 mm . not necessarily recommended but can be done.
Tin