This might be another one of my unpopular opinions, however, this is what I see happening when a dog is leash-reactive:
They see something that arouses their sympathetic nervous system. So that means they either want to chase a squirrel, they want to meet and play with another dog, OR they are actually feeling extremely nervous about potentially meeting another dog or a strange human. So your dog either wants to HUNT, chase, or play, and all of these things cause barrier frustration due to be restrained on the leash; or they are put into a state of fight/flight by whatever their particular trigger is. The reason that we want the dog to move and express that energy by either barking or pushing or playing tug with the owner is because there's a buildup of that sympathetic, flight/flight energy again, due to not being able to naturally move they way they would if at liberty.
If your dog is in a state of drive, those particular core exercises will channel and ground their drive (desire) to hunt, play, and chase whatever stimulus has caught their attention. If your dog is going into fight/flight due to a reaction to their trigger, then the build-up of that energy is made more intense by the restraint of the leash and they are forced into "fight" because they obviously can't flee. There's a bottleneck of that energy that can make these dogs explosive on leash, like shooting water through a hose. Those SAME exercises will channel and ground this unresolved emotional baggage by putting the dog in a state of drive and draining that energy to ground (to the handler who accepts the emotional "charge" by becoming a sort of lightning rod).
So you have a dog who is in a high state of arousal, and because we have the dog on a leash, their movement is restricted so they can't express that energy in way that would feel really good to the dog. I see a lot of people then put their dog into a "sit" and ask for "eyes on me." The problem is, you are further restricting their movement! And you might actually be inadvertently putting your dog into a FREEZE response, which is actually an even less desirable response than fight or flight. Normally the nervous system only goes into freeze (think of a possum playing dead) when the nervous system calculates that the animal will not survive the interaction if utilizing fight or flight. The very last option we have is to freeze. Now your dog is like, oh shit, this is dangerous, I guess I will check out and play dead (dissociate).
Sitting still in the face of danger, arousal, prey, play, etc. is SO unnatural for the dog. You're either going to make the issue worse (especially by forcing eye contact which further stresses the dog with your predatory gaze), and at the very least you are creating conflict between you and your dog who wants to move and relieve the pressure of the situation. The dog no longer sees you as a friend they can count on to help relieve stress.
Alternatively, you could ask the dog to bark on command, you could run with your dog, maw and mirror with your dog (dance and play), give the dog a bite, or have them push for food. All of these things are going to help express that sympathetic energy. Additionally, you are attracting and channeling that energy to YOU as the handler. This regulates the dog's nervous AND you get credit for the good feeling, it's a win/win situation! I hope that makes sense. When the dog's body is telling them, "Hey, it's time to move," and you are in agreement, you are putting yourself in alignment with your dog.
Sitting and putting "eyes on me" does not help the dog move the energy which is quickly bubbling up inside. Let your dog MOVE. If your dog naturally makes eye contact with you, they are looking to co-regulate with you! Help them! Give them engagement, play, contact, and grounding.