I know you are an experienced practitioner of more than one art, and often use you knowledge in your work. You can probable talk circles around me.
But I don't know that I would agree with what you have said. In the TKD I have seen or briefly studied, there was very little similarity between them. Almost no Hapkido has forms. It mainly has techniques for specific defenses against specific attacks. The closest I saw in TKD was some final moves in 3 step sparring had a sort of Hapkido flavor, but most were simply a final block and a counter punch. Moo Duc Kwan had some techniques specifically for multiple attacker defense.
But as to the bolded above, when I taught a 4th degree TKD practitioner, there were several times when I would show him a technique and he would get this contemplative look on his face, and tell me there was a move in a TKD form that had never made sense. There might be seemingly strange foot and waving arm movements. When he questioned it, he would be told it was part of the 'art' of Martial Arts. But the technique I had just showed him was obviously the basis for and the object of the TKD move. That happened at least 4 or 5 times. I then concluded that there were things buried in some TKD forms, the meaning of which had been lost even to high Dan teachers. I wish I had written those TKD moves and their Hapkido techniques down. I didn't so I don't recall them now.
I think this opens up a very interesting conversation. Let me see if I can break my thoughts down. Does contemporary TKD look like contemporary HKD. Nope. Pretty much polar opposites in that one is, more or less, a linear block-punch-kick art and one is more circular and involves a whole host of things no generally seen in TKD. But is that correct? Is that the way it could/should be? Up until about 15 years ago, give or take, I thought of TKD and HKD as two very different arts. And in truth, generally speaking they are the way they are taught. However, there is small circle of folks in TKD that have gone a different path. I feel that it stems back to Okinawan karate.
What follows is a simplistic, reader's digest version of the evolution of karate. In the 1800's, karate was different that what is generally seen today in many/most schools. Itosu Sensei was one of two men that most of the modern Ryus flowed from. He was also a college professor in addition to being a karate master. He wanted to get karate into the school system for it's health benefits. But he realized that you can't teach 'real' karate to kids. So he revamped certain kata, Pinan as an example, into a more block-punch-kick format and left out the chokes, throws, cavity pressing, joint destruction etc. movements. This eventually flowed into the Japanese school system through efforts from Funakoshi Sensei. None of this is a bad thing. It was simply 'karate-lite'. Now, keep in mind that Korea, like Okinawa was a prefecture of Japan during this time. Flash forward to the end of WWII and the Allies winning the war and occupying Japan. By-and-large, those karate masters in Japan/Okinawa start teaching the conquering invaders karate to make a living. And again, by-and-large what was taught was the children's version of karate i.e. block-punch-kick. Parallel this with Korea, which for the most part was had it's citizens as second-class citizens in the eyes of Imperialistic Japan. The average Korean didn't learn 'true' karate either. So you have both the Allied G.I. and the Korean martial artist leaning a specific sect of karate and then taking it back to their home countries and teaching it and passing it on to future generations. Also keep in mind that the block-punch-kick format fits in nicely with sport competitions which is a $ generator for many schools.
Karate practitioners such as Iain Abernethy Sensei, John Burke Sensei as well as TKD practitioners such as Stuart Anslow and Simon O'Neill have delved into the kata/forms to reconstruct/interpret movements/techniques/concepts/strategies that go well beyond what is normally associated with them. As far as Karate kata, looking at what/how they've researched demonstrates information that kata contain a myriad of things well beyond the B-P-K format. Indeed, many Karate masters from various different Ryus stated that one could know all of karate from just one or a few kata. Information that demonstrates throws, take downs, locks, cavity pressing,chokes, escapes etc. In truth, you'd be hard pressed to see the difference between karate and say, Aiki Jujutsu. If you walked into a class that had no specific identifiers you might confuse the two.
Switch gears to TKD and HKD. HKD is generally accepted to come from Aiki Jujutsu/Aikido roots. TKD is generally accepted to come from Karate roots. Except for those that try to pass either off as 2000 year old arts indigenous to Korea. That's bunk of course. So, assuming/accepting that TKD comes from Karate one would make the logical assumption that they share many foundational principles. TKD forms generally date back no farther than the 50's though some reflect renamed Okinawan kata the are much older. So, if the movements in Okinawan kata reflect specific principles such as throws, locks, pressing, escapes etc. in addition to strikes it would stand to reason that TKD forms would contain the same information. I would submit that kata are well constructed paragraphs of information,created by true Karate masters, to pass on to subsequent students. I would further submit, without meaning to offer a slight towards TKD, that TKD forms mimic kata but in many cases were created by those that were FAR less experienced. In otherwords, kata a beautifully crafted paragraphs that convey a story. TKD forms are, in many cases, incomplete sentences cobbled together. Yet they convey the same information in theory even if it doesn't flow as logically. So a specific movement in a kata means something specific, it will have the same meaning when it's seen in a TKD form. It may not be taught that way, but a movement is a movement regardless of what it may be called.
So that's why I don't think TKD forms are as 'clean' as kata. Again, not a slight against TKD. Those early TKD 'masters' did the very best they could with the training and experience that they had. But this leads to the deeper/adult version of Karate. As mentioned, Karate could look VERY much like Aiki Jujutsu in a LOT of it's movements. So I would submit that TKD could look VERY much like HKD if it was taught in the same manner. And that is how it is taught by a small segment. Now I suppose I wouldn't go as far as saying they could be completely indistinguishable due to certain individual nuances in each art. But again, if there were no visual identifiers (like a sign hanging on the wall of the school), TKD can (and is) taught in such as way by some schools to where you'd be hard pressing to label it one way or the other if you just walked in off the street to look at a class.
It's bit of a change in how we think/view a particular art. But I think it's a plus. Your example of a student that was taught a movement in TKD that really had no explanation yet once he started learning HKD saw how that movement had an actual meaning/purpose. Well, those same principles are in the forms, basically just sitting there unused until someone identifies them as actually working beyond the commonly accepted norm. So TKD and HKD are separate arts but TKD could be taught in such a way as to be quite a bit more than what it's generally portrayed as. Let's face it, mention TKD and you think spinning back kicks. You don't think serious joint locks, throws, cavity pressing and all the other HKDish things.
But it could be taught that way. Again, HKD would still have it's own nuances but TKD could generally be more of a sister art with it's own nuances.