You don’t have to drop the nose because flying works the same as a low earth orbit (and any other orbit for that matter)

Picture a tennis ball on the end of a rope which you are spinning around your body. There is a speed required to keep the tennis ball in tension with the rope, and without that forward momentum it would fall.

A plan has a speed which it must travel at in order to maintain an altitude, which is determined by the downward forces acting on it. If it slows down enough, the downward force will start curving it back towards the earth and it will fall. If it wants to climb, you need to add velocity in order to counteract the downward force.

This is the same concept as what keeps the earth in orbit around the sun - the earth is essentially always being pulling inwards towards the sun, but is moving at a rate of speed fast enough that there is an equilibrium and it maintains a constant distance.

Ironically, while these dynamics can be naturally observed, our orbit is so perfect for life that many have used it as an argument for god. It’s really selection bias, but the flat earthers are completely wrong about the globe being a concept pushed by only godless “globalist” who want to remove spiritually from the world. Most modern science came from Christian’s who wanted to explore and explain gods creation.

There are a few things wrong with this argument.

That is not how planes work. If you ask that to a pilot they will tell you of course they don't because gravity makes their plane follow the curvature (and look at you funny because they are thinking "surely they are not a flat-earther right? that would be silly")

You don't feel the drop because you are not dropping. You only feel change in height when you oppose gravity, and as long as you keep the distance to the center of earth the same, that doesn't happen