Assuming your question is addressing this point:
it seems like no one is actively pursuing this technology
I think there are multiple reasons for this
It's too early for orbital-lift infrastructure.
Only in the past couple years has a major private/public interest in space re-emerged as it may have been present during the space-race and Apollo Era. I don't think it's unfair to say that this is almost entirely due to SpaceX. Regardless, we are just now seeing entrepreneurs starting to seriously consider space as a market and an opportunity that can be tapped, but we are still many years out from a space industry that doesn't rely almost entirely on government subsidy in some form.
For it to make sense to build infrastructure, there needs to be an active need for it, and, as it stands, we are still in the rapidly-climbing part of the s-curve when it comes to rocket technology. Right now, a F9 runs like \$1.5k per kg to orbit, and if the design and performance goals of Starship are met, I don't think it's unreasonable to drop this by a factor 10 to a blistering \$150 per kg.
This is so cheap, that assuming it pans out, it won't be unheard of for high-achieving high-school students to launch satellites into orbit as science fair projects in the 2030s.
Now, with costs reduced this far, it is likely that we will be approaching the limit of rocket-based Earth-to-LEO in terms of optimization. We've had airlines for many years now, and while there are still steady improvements, a 20 year old commercial jet isn't that different in performance to a brand new commercial jet. Sure, a couple percentage points here and there along with nicer and more comfortable features, but it is definitely a technology that has reached the top of the S-curve and requires a new breakthrough/paradigm to move forwards.
This is the point where a new system, like skyhook would make sense. Guesstimating, you could probably beat the efficient reusable rocket model (like Starship) by another factor 10, bringing the per-kg prices down to low two-digit dollar figures (\$15). Doing so however only makes sense if there is an enormous market demand for it, because infrastructure is expensive.
This is where going orbital costs about as much as a plane ticket does today, and a world where the average human goes to space about once every two years (right now, there's a world pop of about 8bn, and about 4bn passengers fly commercial every year).
We are still... many decades away from this.
People are already working on this.
All that said, there are already scientists working on this. Not directly as skyhook, but working on elements that lead to it in the "technology tree".
Specifically, there have been many "tether"-based experiments involving small-sats and the behaviors of tethers in microgravity, which rather directly translate to skyhook tech.
Similarly, one component of the earth-to-orbit skyhook system is the spaceplane. Here, multiple groups are working on systems that may one day serve as a base or provide the engineering underpinnings for such a system like SNC with the Dream Chaser or the British team that's working on the SABRE engines.
There are also more general developments going on that lead to the development of more advanced orbital systems. One somewhat-shocking fact is that there are basically no autonomous satellites right now. Despite highly automated systems for eg traffic management systems, basically all LEO satellites today fundamentally rely on constant command/control from the ground to function. Some space startups, like Privateer, are trying to fix this by building the autonomous satellites that actually make decisions and operate independently in space, without relying on constant commands from the ground. This will also be critical in any form of advanced orbital infrastrcuture.
Skyhooks are technically more difficult to understand.
This one is a bit "dumb", but one of the reasons why "Space Elevators" are as popular as they are despite being riddled with fundamental issues, is because the concept is dead-simple to explain. Everyone's ridden an elevator before, so if you tell someone you plan to build an elevator that's just really, really, tall, they more-or-less get it.
Skyhook, meanwhile, is much more complex. It requires at least a KSP-level of understanding about orbital mechanics (which is actually quite a bit) and a good grasp of high-school physics to even "get" the core concept (nevermind the more technical foibles). This makes it less attractive and more difficult to communicate.
If you'd like to start campaigning to address this lack of public knowledge about the topic or industry excitement about skyhook tech, go right ahead, but I think your energy would be better spent on fundamental science communication which brings ordinary people to the level where they could understand it to begin with.
