For some reason, I can't get that video to load. Here's my thought from what I've seen of wrestling and Aikido. Most Aikido schools only train an upright structure and variations from it. Wrestling (and Judo, to a lesser extent) often gets into a bent structure from the start. That will cause real problems for someone who has only trained that upright structure. Now add that most Aikido training depends upon direct input. Grabbing an arm and staying still (part of hand fighting, for instance) doesn't feed the weight shift they depend upon, so there's another problem.
They have throws both entering and exiting, both front and back (for the person being thrown), but not much for tight clinch distance. There's plenty of related material that would flesh that out - imagine adding some basic Judo to it. This is why I see Aikido as a sort of "finishing school" - a way to put some polish on movement for someone who already has a solid base. Someone with solid Judo skills might find Aikido expands their options, and they would already have the skills for handling both resistance and input (the latter getting expanded more by the Aikido).
This is a bit more what NGA is. We have some influence from Judo, and I bring that more to the front than most instructors (Judo was the first art that seemed to click for me). I do actually train both aiki and "hard" (Judo-type) throws similar to what you recommend. After I teach a technique, I show the common resistance points and what would be available at each. When showing a technique that depends upon resistance, I follow up with the reverse - what is available if that resistance isn't there or is too weak to feed the technique.
I think there are a few misconceptions here. It is true, that we do not start in a bent structure. This has a lot to do with the concept of Zanshin. I would say, that for on armed, 1 on 1, combat, there are number of Arts that are better than aikido. However, we make 2 assumptions that most arts do not make. 1. every attacker has a weapon. EVERYONE has a weapon. Could be a bottle, could be a pool cue, could be a stick, could be a knife, could be a glass, there is always a weapon involved. 2. every attack or has friends. The fight will never be fair, and will never be 1 on 1. We assume always, that there will be another person joining the fight.
In those situations, when you are fighting against weapons or multiple attackers, Aikido is likely a better choice than many other arts.
Also, we could create the weight shift if we need. At lower levels, we train in a static, non dynamic manner. People have to feel and explore the movement of the technique. For example, I was working with a junior student the other night on shomenuchi ikkyo. He was struggling, as he kept trying to push my arm in a linear manner. I resisted, and demonstrated that he was not doing the technique properly. I showed him how to employ a circular motion that worked around the resistance. We always discuss where the resistance is, and how to work around it. At higher levels, the techniques by necessity have to become dynamic. Concept of sen sen no sen. You should already be moving before your opponent even touches you. This way, resistance can never be established. It takes a long time however to get to that level.
As far as creating weight shift, this is where atemi becomes so valuable. O'Sensei once said that 90% of his Aikido was atemi. What he meant by that, was reacting to an attack before it lands, and using strikes to off-balance your opponent before throwing. Unfortunately, most aikido dojos do not practice this. That does not however mean that it is not there.