You're not answering the question, which is specifically about cardio and how to train to build the biggest engine. You're correct that those positional exchanges and the technique and savvy to win them are more important than having slightly better cardio. Yes, the guy who takes superior position is going to exert less energy but that has nothing to do with the question of how to optimize cardio.
You again bring up jogging. I'm not arguing in favor of jogging. I had a similar discussion about this with my wrestling coach who said that the work McGregor did with Ido Portal on balance beams, olympic rings, moving in strange ways, and playing touch butt in the park was stupid and should have been used to improve his weak area of wrestling.
You should spend your time doing the activity(ies) that you're specifically trying to improve at, whether it be wrestling, boxing, mma, or jogging. What I'm advocating, and you don't have a lot of knowledge about, is the implementation of training zones, training blocks, micro cycles, macro cycles, periodization, aerobic base training, threshold training, and anaerobic interval training. I don't think you're familiar with some of these concepts. The principles behind them can be utilized in just about any sport.
It's more challenging to use zone specific training in wrestling and combat sports because of the dynamic and irregular nature of training with a partner. Really you need a heart rate monitor and partners and coaches who understand what you're trying to achieve in a training session, but the benefits of training with a focus on systematically improving a specific energy system for a month or two at a time and then building upon that is big.
In cycling or running, it's easier to quantify training zones. It's very straightforward in both sports. With running, you run at varying speeds and measurements are taken. With cycling, in a performance lab setting, they measure by power or the number of watts generated at any given time. EVERY serious rider in cycling trains with both a heart rate monitor and a power meter. Determining an athlete's lactate threshold, max heart rate, and vo2 max is fairly simple.
How do you imitate this kind of a controlled environment where power or output, oxygen consumption, and blood lactate can be measured in a combat sport? You can't, but that doesn't make performance measurements of this type and training zones established off of those numbers useless.
Testing begins at about 2:20 into the video
Getting numbers like these from a treadmill or stationary bike can help you determine training zones that, with a heart rate monitor or going by feel for an experienced athlete (very easy, easy, tempo, hard, all out), will enable you to build your aerobic base to a greater level than just going easy or blasting. You and many martial arts coaches are still in the dark ages when it comes to the higher level science of building cardio.
My wrestling coach also talked about wrestling at different intensities and being able to try new things that you can't do when you're always rolling at 100%. He said Dave Schultz used to train this way a lot in a less intense flow roll style. If you have partners and coaches who understand the objective of the training session, it's possible to target specific energy systems even in a less controlled sport like wrestling or mma (compared to cycling or running).
Does that mean that it's not extremely important to know when and how to use proper technique to blast your way into a superior position so that you can use less energy than the other guy from there on in the match? No, but all other factors being equal, you should still strive to maximize your athlete's cardio in addition to proper technique and strategy.
Also, different subject entirely, but if you're a heavyweight and don't need to cut much or at all, then I think it's not a big deal to carry some extra fat. It can actually help cushion and protect you and make you less likely to be injured compared to a lean guy who is mainly skin, muscle, and bone.