To answer your specific question, no, there are no technical impediments.
That said, there are reasons why passive components are still used.
As you might have guessed, cost is potentially the biggest reason active suspensions are still uncommon. You mention some applications where cost is less important (it's never unimportant), but consider cost per performance vs simple cost. A well designed passive suspension will handle a majority of driving cases, will only have a single resonant frequency (ignoring harmonics, which are hard to activate on a vehicle), and generally perform well to minimize NVH. These systems cost very little to implement because we've used them for quite some time now. As such, incremental gains to existing passive suspensions don't require extensive investment and always provide increasing levels of performance. The cost per performance, then, is minimal.
On the other side, active suspensions allow for perfect body control. You can completely isolate the cabin from any wheel movement. Of course, doing so requires a multitude of sensors and actuators that the car wouldn't normally have, and that cost significantly more than their passive counterparts. There's also the cost of developing a control system (you can't just throw a PID controller in there), and robust actuators in a small enough package for the vehicular space requirements. All of this is feasible but costly. For all that investment, you get (perhaps) an order of magnitude attenuation on top of any passive systems? 10dB isn't terribly impressive under most driving scenarios, so unless you are switching driving styles/surfaces significantly, it's not worth it.
For lack of a better term, it makes no sense to go full active when you can complement a passive suspension with an active suspension (ex. ClearMotion). This significantly lowers development cost while providing the same (or better, as we'll soon see) gains as a purely active system. To provide an analogy, you are effectively saying, "We can model a resistor with a suite of transistors, so we should replace every resistor with this suite of transistors." Yes, we can. No, we shouldn't.
I don't consider this a technical impediment because power can always be made available, but active systems require absurd amounts of power. Imagine how you would replace a spring with active components. Electromagnetic levitation? Lead screw with strain gauges? Any method of replacing a passive suspension with an active suspension will consume enormous amounts of energy to do the same job.
I don't have the source, unfortunately, but ClearMotion (formerly Levant) systems could only sustain a 1g turn for approximately 10 seconds before the system had to deactivate to prevent overdrawing the electrical capacity of the vehicle. Sure, that's quite a high load for quite a while, but imagine a particularly turny road. My Focus EV owner's manual actually says in it that the power steering rack (electronic, of course) will decrease steering assist if you turn too much because of the power requirements (and overheating). That's a power steering system, which doesn't require nearly as much power as a semi-active suspension. You can always get more power to the system, but at some point, you need to ask whether or not it's worth it.
You mention reducing weight. The best way to do that would be to use newer composite springs with lightweight dampers. That's pretty much all there is to the system, so that's all the weight it adds. Conversely, an active system needs large conductors to power it, possibly air compressors for air springs, electromagnets for magnetorheological damper fluids, travel sensors, etc. Some add to the unsprung mass. Some don't. Either way, you can end up with more weight, especially if you factor in power generation in the form of a larger battery, supercapacitor, or a bigger alternator.
So while we can solve the technical challenges, they aren't challenges that are really worth solving.