Planck length as the known minimal length scale

 When I was a freshman, I was briefly taught the concepts of Planck units in the college physics course of mechanics. For example, there are three fundamental physics constants in nature: Planck constant in quantum physics $\hbar$, Newtonian constant of gravitation $G$ as well as the speed of light in vaccum $c$. Simply by the dimensional analysis, one can construct the following constants that have the dimensions of mass and length (called Planck mass and Planck length): \begin{eqnarray} m_p &=&\sqrt{\frac{\hbar c}{G}}\sim 10^{-8} kg \,,\\  l_p&=&\sqrt{\frac{\hbar G}{c^3}}\sim 10^{-35}m\,. \end{eqnarray}

Besides its small value of $10^{-35}m$ , why the Planck length is said to be the known minimal length scale? I recently found a simple argument from Prof. Hong Liu's lecture notes on AdS/CFT that one can never measure an object's position precisely within the error smaller than the Planck length. Given an object with mass $m$, there are two associated length scales, the reduced Compton wavelength $\lambda$ and the Schwarzschild radius $r_s$: \begin{eqnarray}\lambda &=&\frac{\hbar}{mc}\,,\\ r_s &=& \frac{2Gm}{c^2}\,.\end{eqnarray} The reduced Compton wavelength comes from the uncertainty principle $\Delta x \Delta p \geq \hbar / 2$ in the quantum mechanics, which imposes a limit of measure precision because of the quantum effect. Meanwhile, the Schwarzschild radius is the event horizon of a Schwarzschild black hole in the generality relativity. An observer cannot probe the region inside a black hole. For those who are not familiar with general relativity, the Schwarzschild radius can be argued in the Newton's law of universal gravitation by letting a star's escape speed equal to the speed of light.

If the object's mass $m$ is very small, the precision of the position measurement will be first blocked by the quantum uncertainty principle. On the other hand, if the object's mass $m$ is very large, the precision of the position measurement will be first blocked by the black hole horizon. As a result, there exists the minimal length scale of measurement at which $\lambda \approx r_s$. This happens when $m\approx m_p$ and $\lambda \approx r_s \approx l_p$. 

In sum, at the scale of Planck length $l_p$ and Planck mass $m_p$, both the quantum effect and gravitation effect are significant. This is the region of unknown quantum gravity, i.e., the boundary of the known physics laws. In contrast, the classical gravity (general relativity) is in the region $m \gg m_p$ and $ r_s \gg \lambda$ where quantum effect is not import, while the quantum theory without gravity is the region $m \ll m_p$ and $\lambda \gg r_s$.