First, let me echo everything John Mohan said - with some minor additions. It really bugs me to hear people defeat their own growth potential by saying, "I'll never do this or that". If that is indeed your feeling, you won't. We must, in all aspects of our lives strive for excellence and work towards that goal each day we are allowed the privilege of getting up and going about the day. It is never truly over till its over. Maynard is attributed with saying something like, "We never learn to play the trumpet. It is a life long endeavor." If you ever visited Jim Manley and been blown away by the things he can do with the horn and you hear him talk about investigating ways to do more and better, it would mess with your mind. If I understand correctly, Doc Severinsen practices hours every day to maintain and advance his skills. That said, since the rest of John's post is so good, I'll only add to it.
And my exception is not really with it - but with what some people might interpret. The phrase "High notes are INEVITABLE, if you're practicing correctly" is a Pandora's Box if you don't take the entire sentence to heart. People practice pedals, breathing, yoga, TM, the Tasteebros Way, 7 C's, Maximizing Daily Practice, Adam Routine, Cichowitz Flow Studies, Pops method, Brass Tactics, Clarke studies, Arban, long tones, you name it and get no where. There is that little key of "correctly" that sits in the way. Most books I read have gone to great lengths to tell you "how" to practice their ideas, but a lot of times students fail for a variety of reasons. One, that is a key element in Mr. Jacob's (and I think Mr. Adam's) approach to playing is the sound. There is so much truth to "It is sounds great, it is being done correctly". The problem lies in being able to distinguish an acceptable sound with a great sound and being able to know when you are producing a great sound. It becomes a matter of perspective. If you are 1st trumpet in a good 7th grade band and play better than everyone around you, you may develop the illusion that you have a great sound. Indeed, if you are the best player you have access to, then you will probably work from the mistaken idea that you are really there, sound wise. Most of us on the list have dealt with students that appear with a standard trumpet player ego from being top fish in their little pond with no idea that there is such a thing as the lake or just how big the fishes out there are.
To address Rich's question with that said... Yes, you need to practice up there to be able to play up there - BUT! If everything below it is not easy and with a great sound, then you are working too hard and not learning muscle movements (developing the correct neural pathways - programming your own bio-computer/brain) that will be conducive to being able to play up there with the freedom and power you desire. We want this to be as easy as possible and sound as great as we can sound. If our top of the staff G sounds pinched, that problem needs to be taken care of before we start practicing in the uppers BECAUSE what is stopping your mid-highs from being easy and sounding great is the very thing inhibiting the development of your range - hence a little different slant on "practicing correctly".
The Clarke approach to playing softly has a great deal of wisdom! Jim Manley likes to demonstrate just how little air it takes to get the trumpet to respond by lightly popping the mouthpiece with the hand. You will hear a pedal C pitch come out the bell. If the trumpet will respond to very little input, then we don't need to be blowing the walls down to play. Most of us overwork when we play the simplest things. The method behind playing the Clarke Studies softly is to get you to ALLOW the lips to vibrate with very little work. The open mouth/throat, breathing with a "HO" or coughed "HO" (except not as violent) approach (gets the air moving from the bottom of the torso), firm corners, and a loose embouchure center will allow this to happen. Mr. Jacobs said on many occasions, "The first point of resistance to the air is the lips". They are the valve. If you have the tongue high/teeth together/jaw closed, you will have to blow against this resistance to get air to the lips. The air will then be under pressure and the sound tight (more pronounced on soft, high passages).
Jim has really been an inspiration (and Scott Englebright on IRC earlier) getting me to think about making it easier to play - more relaxed. That challenge has been the focus of every change I have made in the past 9 months - and I am still changing things looking for an easier way - AND IT JUST GETS EASIER! It is no small surprise that former students of mine have been remarking on how my sound is so much better than they have ever heard me play. So, what does this boil down to? John was right. Actually, knowing what to practice is not nearly as important as knowing "how" to practice. If you know the "how" the "what" will take care of itself. This also comes with a self-critical analysis of being able to say "My g in the staff is just too much work. I need to allow that to vibrate easier." or "I wish my sound in the staff was more resonant.".
It is possible to play and practice pedals incorrectly! I did so for years. Learning to play an in tune, centered pedal C was a first step for me. Trust me, you don't have to lip it up when you are doing this right. With Jim's guidance, I am constantly discovering ways to change the pedals so that they sound more like the resonant, centered pitches an octave higher. Then, it becomes the trick to transfer this approach to the next octave - and the next octave - and the next... When you get on the right path with your practice, everything just gets easier and easier. I got my first centered, "legit" double C about a week ago with my one week old embouchure shift. I had not been working on the that range, it just appeared one day in warmup. Michael Haydn, here I come!
Enough for now - sorry for the epistle.