The general problems are the design trade offs that occur any time when there is a direct mechanical linkage between the internal combustion engine and the drive train. The reason is because you are most likely forced to use an engine that has some greater variability in torque and rotational speed than would be necessary if there was no direct linkage.
Why does this matter? Because it likely reduces overall system efficiency. For maximal efficiency, you are better off having an engine that is custom paired to the generator, meaning that it runs at a very confined torque range and rotational speed to maximize generation of electricity since electrical generators generally work most efficiently at a specific rotational speed and fall off on either side of that speed.. This of course requires that the amount of electricity generated is enough to drive the electric motors alone (i.e. no battery support in the case that the battery is dead). By adding a direct mechanical linkage, the engine is likely to require operation over a wider range of speeds and torque and is less likely to be optimized.
Why all this "likely" talk? The video I linked to is the first in a series of presentations by Pamela Fletcher, the head of GM's electric drive train division. She talks about the trades and the systems design that led to what we have now; it's really pretty interesting. Basically they started out with exactly what you want: a traction motor driving the wheels directly, and a generator motor attached to an ICE, with only electricity flowing between them. Then they said "hey wait a second, electric motors are less efficient at higher RPM; can we use this second electric motor to reduce the speed of the first through a high gear ratio, thus improve overall efficiency at high speeds? By golly we can!". That is why the generator motor is able to couple to the traction motor at high speeds to drive the wheels together.
The fact that there is a mechanical linkage when you then enter charge deplete mode is actually a by-product of wanting the ICE connected to the generator motor, but also wanting the generator motor connected to the planetary gear set. It's not something that was baked in from the start as a "core ideal" or goal, it was something that came about as the result of a number of other trades.
The biggest downside to going this route is that there are intermediate periods of time where the ICE will be free-wheeling, which means they required a throttle assembly. If the generator motor were always attached to the ICE output shaft, you wouldn't need a throttle, because you could just cap the RPM using back torque from the generator motor.
Based on the specific conditions that you had indicated for when the mechanical linkage occurs (constrained torque scenario), it is possible that they were able to marry the best of both worlds in terms of efficient engine design, but I'm skeptical. Also, this setup would presumably mean that the individual drive wheels are not directly driven by electrical motors and that there is a drive shaft and differential of sorts in between the electric motor and the wheels. This likely also reduces overall efficiency than a direct drive scenario (i.e. electric motors directly connected to the individual drive wheels).
After warming up, the ICE is generally operating at wide-open throttle (peak efficiency for a given power output). Its RPM is capped by the torque put on it by the generator motor and, when in that situation, the planetary gear set. By adjusting the flow of current (and thus the torque) between the two motors, and using the battery as a buffer for transient events, they can adjust the output power of the engine simply by adjusting its output RPM. Keep in mind that the electric motors are not lossless and neither is charging/discharging the battery. Any power going from the ICE output shaft to the drive shaft mechanically is not subject to the losses of going through two electric motors (one to generate the electricity, then a second to turn that electricity back into mechanical energy).
In almost every vehicle, the wheels have independent half-shafts that are connected to each other and to the main drive shaft via a differential. The design of this differential is sometimes different (open vs limited slip vs Torsen, etc.). This applies for pretty much any mass-market vehicle you can think of. The Volt was never looking at individual drive motors for each wheel (neither did Tesla for the Roadster, S, D, or X; do you think there might be a reason for that?).