thermodynamics - Why does hot air rise in a column instead of cold air pressing down?

Ok, this looks like a dumb question or even near trolling, but I really don't understand it.

When air is heated over an oven plate, it rises. Obviously, I can check by blowing some smoke in.

The common explanation is that hot air has less density than cold air, and consequently, it rises.

Fair enough, the hot air will end above the cold air, but why is it rising in a column?

With the same argument, I could deduce (and I know that it's wrong) that the cold air above is denser, so it will go down, pressing the hot air away sideways.

What additional fact am I (and the common explanation) missing?

(I'm pretty sure that the tags I found are not optimal.)

Edit: in my mind I envision a picture of (red) hot air molecules separated more than the (blue) cold molecules which slip down between the red ones. I'm aware that this is a very crude model, and moreover ends in a wrong prediction.

Edit (about the duplicate): I'm not sure if the other question is about the way in which the hot air raises. At least, the answers over there do not (or not clearly) address this aspect.

The accepted answer here explains what is going on by stating formulas for pressure above the heat plate as well as next to it.

Answer

You ask why a column of hot air (as in a chimney) rises, given that denser cold air is above it, pushing down. It rises, because denser cold air around the BOTTOM of the chimney is under higher pressure than the cold air at the top of the chimney. The extra pressure due to a chimney-height of cold air is pushing it down. The lesser density of hot air means that the chimney-height of hot air causes less pressure than the surrounding cold air.

In formulae, the situation is: outside the chimney,

$$ P_\textrm{(chimney-top)} + \rho_\textrm{(cold-air)}\cdot g \cdot h_\textrm{chimney} = P_\textrm{(cold-chimney-bottom)}$$

for the cold air, and inside the chimney

$$P_\textrm{(chimney-top)} + \rho_\textrm{(hot-air)} \cdot g \cdot h_\textrm{chimney} = P_\textrm{(hot-chimney-bottom)}$$

where '$\rho$' is the density of the air.

$$\rho_\textrm{(cold-air)} \gt \rho_\textrm{(hot-air)}$$

Thus, the cold air at the chimney bottom is higher pressure than the hot, it pushes its way in, and the hot air is displaced (it rises).