I'm just saying to help slow it down a bit to gain a couple of seconds or so of time to sort things out and not to land the thing with. Drogue parachutes are a bit different from normal parachutes
A drogue chute would have zero effect on this thing. It's about 125 metric tons. You could use one of those M1 Abrams parachutes that kicks a heavy vehicle out of a C130 on a runway, it wouldn't be worth having. In fact, a chute on the nose, even if it could hold up to the stresses and contribute in a meaningful way, would probably exacerbate the problem here.
The problem is partially the speed, but it's more around the over-correction of orientation due to Thrust Vector Control controlling the maneuver rather than Reaction Control System doing it.
The current RCS on these things is pitiful. It's cold nitrogen compressed gas. It's not nearly enough to spin a steel building 90 degrees in a handful of seconds, and then stop that spin once perfectly vertical.
So what they're doing instead is using the Raptors. When you light those things while it's horizontal, you get a bunch of horizontal velocity while you try and rotate its attitude. That has to be negated. What we see is the rocket rotate about 120 degrees, the TVC overcompensates in the opposite direction and cancels the horizontal velocity, then tries to come back to vertical again.
The center of rotation is closer to the nose fins while it does this. You have to compensate for the angular momentum of nearly the whole ship, plus gravity, all at once.
SpaceX has a goal of putting hot-gas thrusters on this thing. Tiny little methane/oxygen rocket engines similar to Raptor but much lower thrust. Still way higher thrust than cold nitrogen though. Using those will allow the center of rotation to move lower on the vehicle, rely on TVC of the main Raptors less, and reduce complication of the landing burn calculations. And it would also hopefully avoid the over-correction issue entirely. You can't avoid it if you're using your main propulsion engines to rotate the whole craft 90 degrees.
One other problem they're having is maintaining proper fuel pressure. During ascent this thing sucks fuel from the main tanks, right above the engines. But at the landing maneuver, fuel feed is shifted to alternate smaller tanks. One is in the nosecone and the other is nested inside the main tank (can't remember which is O2 or CH4 and it really isn't relevant to the problem). There is less slosh during the horizontal-to-vertical maneuver if a tank is full, and these landing tanks are tiny compared to the launch tanks. The Raptor engine is supposed to be able to autogenously pressurize these fuel tanks with a little bit of exhaust, to keep the fuel supply steady. That's not working quite as expected, so they are augmenting that with COPV canisters filled with nitrogen or helium or something, to boost gas pressure in the landing tanks.
Parachutes are just not the answer to this problem. A parachute of the scale to have any impact on this vehicle would weigh more than several seconds of fuel to burn to impart more authority to the landing maneuver.
