It was a rhetorical question, and I didn't want to turn this into a discussion on tactics. But since we have two different answers from pilots of different skill levels, it might be worthwhile to point out the general differences.
Had Yarbles tried that vs me for example, I wouldn't have followed him low and slow. I'd have let him drop if he wanted, and simply picked him later when it was convenient and he'd lost his speed. Not because I wanted to pick him, but because he'd be "no threat" anymore, and I'd shift to planes that mattered. At this point his tactics are far from aggressive, so I'll put him in my category of "keep an eye on him, but look for bigger threats.
A) Kill the biggest threat first. He's not it, since he is willing to drop alt and E, it gives me a big hint as to his skill level and/or intentions. If he see's me not following and decides to come back up, he'll be in a bad position to deal with me. If he flies off the map and comes back above me, so much the better. I can dodge high planes 'til the cows come home, and the alt may make him feel confident enough to get himself in trouble.
B) I only put in the amount of effort required to shoot the guy down. If he wants to drop and make things easier for me, I'll put in less effort (I'll pick him). If he makes that difficult, I'll put more effort into it as well.
C) Following him low and slow puts me in a bad position for my next kill, especially if he's heading toward his field/ack. I don't need to stay high, but I don't want to be swarmed on the deck either. Having too much alt can be almost as bad as too little, unless sight-seeing is my goal.
Saxman though- he's a problem. He's trying to bleed my energy advantage, all the while maintaining or increasing his altitude and E relative to mine. It's going to take more effort to beat him, and it's going to be much more important that I do so. I can't let him go away like I can the guy who fights as Yarbles describes. I'm going to need to put a lot of pressure on Saxman to keep my advantage and press it home. Extending and giving him room to breath would be a bad idea. The fight may end up on the deck, but not right away. P51's can be beat up high too, and it's more advantagous to both of us to keep the fight high. It helps keeps the fight "private" if nothing else.
The difference is that Saxman has LEARNED how to deal with difficult situations, and can often reverse things in his favor. He didn't learn that by leaving when things got bad. He also didn't learn it by getting beat and not figuring out WHY and how to change that result. Getting beat (or winning, for that matter) IS pointless if you don't/can't learn from it. He's using more complex tactics that require more practice to master, but yield better results in the end. That also hints that if his initial "plan" doesn't work, he'll recognize that early enough to try other tactics. He didn't run away when the teacher pulled out the algebra book.
Personally, "living" is important to me as well. I'm not telling you to dive into the slaughter mindlessly. I take the most enjoyment from beating someone in a "fair" fight, and "living" to land my kills. Getting shot down is not equal to shooting him down, IMO. But picking someone for a kill isn't equal to beating him in a decent fight either. Picking is something I do while waiting for a decent fight, kind of like eating peanuts in a bar. Better than nothing I suppose, but not all that satisfying. Picking will never go away, but hopefully it won't become the "main" way of fighting either.