Doing suicides, where you sprint as fast as you can for long intervals builds two things. Your Anaerobic endurance, and your anaerobic strength.
Anaerobic endurance, basically is your threshold, how much work you can do without exercise.
When you perform something anaerobically, it means your respiring for energy, without oxygen, the problem with this is that it produces a harmful biproduct, called lactic acid, that fatigues your muscles and therefore performance suffers. Your Anaerobic threshold is how well your body copes with lactic acid, and how quickly it recovers between short bursts.
I'm not disagreeing with you, this is an essential part of training, because recovering quickly between short bursts is a quality all top footballers have. But it isn't going to do you any good if your doing aerobic work.
Aerobic work is when your body is using oxygen for energy, and is typically normal day to do things at lower intensity for prolonged periods of time, like walking and running. It produces a lot more energy, and there is no harmful by products. This is why you can run miles, but struggle to sprint a whole track.
The reason people do heart rate training, is because your body flips into anaerobic mode, whenever your heart rate exceeds a certain level, this is generally above 80% of your max. Below this however is aerobic, and doing aerobic work does many things.
It increases heart strength significantly, allowing it pump harder for longer. It increases lung volume, allowing you to get more oxygen. It increases your body's transport system as a whole, to make it more effective and efficient. It also stimulates the growth of red muscle, or slow twitch fibres, which are more adapted to low intensity, long duration exercise.
As you can see, there are a lot of benefits to this type of training, but I agree with you, all types of training are needed to be a top footballer.
And aerobic training decreases your anaerobic strength, because it encourages your body to break down fast twitch muscle fibres (white muscle) and produce more slow twitch, which means your endurance goes up, but your speed and strength suffer due to less fast twitch fibres.