Of course I have to comment on this, as an avid collector and enthusiast of trumpet exercises.
The challenge and the reward of playing a brass instrument is that the production of sound is so personal, and is so closely related to our bodies. Our bodies feel different every day, and so does our playing. We must constantly re-learn how to produce the sound, and always strive for more intensity, complexity and expression coming out the bell.
Exercises target the production of sound and improve our ability to play a good note in any register, at any volume, at any time. It can be difficult to find pieces of music that will take you just to your personal limit and perhaps a little further. Exercises are progressive, they make us reach for just a little more each day, and in this way we improve gradually, absorbing the daily lessons.
There are two common errors in the practice of exercises. The first is to play too much, too soon, too loud, too high, too fast. In the pursuit of one ideal, e.g. high notes, we ignore another, e.g. tone quality. Every note in every exercise should be approached with the goal of playing a beautiful tone, centered, controlled and musical. Practice slowly, carefully, softly-listen for the flaws in your sound and take the opportunity to improve it.
The second mistake made when practicing exercises is to approach them like a necessary evil, a drudgery to be gotten through before the music starts. If you approach a practice session with this attitude you will reap few rewards. If, however, you approach a session of exercises with the idea that you are developing your sound, and thrill to the difference that focused concentration can make, this will translate into improved performance in everything you play.
When I first start to play in the day I often have a sense that my sound is not yet happening. I use exercises to try to bring it to life, to re-learn the sensation of vibrating my lips at each frequency, and of controlling those vibrations with my air. I am not thinking unduly about the muscles involved, but I am devoting full concentration to the sound I am producing, and I constantly search for the physical processes and adjustments that will result in better sound. Exercises are by their nature simple in composition so that we can devote full concentration to the sound. When we move on to more elaborate compositions ('music'), we can relegate the trumpet processes to the subconscious level, and focus on the musical message we are trying to deliver.
Technique or chops for its own sake is meaningless. The vision must always be music. Exercises can help us achieve mastery over the instrument. The greater the mastery, the greater the chance we have to realize our musical vision.