Is it possible to fly a Straight and Level flight at high speed?
Yes, with good engines and low drag you can fly straight and level at really high speeds.

What about the AOA? It gets smaller, but only down to a certain limit. At level flight, the weight of the aircraft is equal to the aerodynamic lift:

$$ W = L =C_L\cdot\frac{\rho}{2}V^2\cdot S $$

The lift coefficient depends on the AOA ($\alpha$):

$$C_L=C_{L0}+C_{L\alpha}\cdot \alpha$$

Therefore,

$$\alpha = \frac{1}{C_{L\alpha}}\left(\frac{2W}{\rho V^2 S}-C_{L0}\right)$$

For very high speeds the first term of the parenthesis will get close to zero, so that the desired AOA setting becomes

$$\alpha_{V\rightarrow\infty} = -\frac{C_{L0}}{C_{L\alpha}}$$

This AOA is indeed negative for most aircraft. If your AOA gets smaller you won't be able to sustain level flight.

The plot below shows the AOA needed for straight and level flight on a Cessna 172 and compares the two terms in the parenthesis of the equation for $\alpha$ (multiplied by 10 for better readability). You would need to fly much faster than $V_{NE}$ to get the first term significantly smaller than the second one.


Source: own work with data from Wikipedia and polar.