The notion that tightly slotting horns are easier to play in tune is a myth in my world. We do not play "well tempered" we play relative to the other notes. This is called "just tuning". We need the horn to respond evenly because we need to bend the pitch to stay in tune in relation to others.
The notion of how a horn "slots" has more to do with how well we hear ourselves. In an overly reverberant bathroom or staircase, an instrument will appear to slot better than that same instrument when played outdoors on a cold day. If we insert earplugs (in our ears), the horn will slot noticably worse than if we just got our ears cleaned.
Sure, we want instruments that can securely be played in tune. I believe that the physics of resonance place limits on what works. I also would not agree that heavy instruments necessarily have less overtones. My heaviest trumpet is the one that is most easy to play and projects the best. It is the most brilliant too.
In many cases, we can improve instruments that are difficult to play. This can be accomplished by moving braces, cleaning the grunge out, aligning the valves and to a certain extent improving the mouthpiece shank/receiver connection. Sometimes a smaller mouthpiece can make our sound get to our ears more easily. I have had several students wanting to get a "darker sound" that ended up just being mushy. Recording their sound with various instruments can prove to them that they were following a "less worthy" goal.
Heavier valve caps on instruments not designed for them can make resonance more stable but as a rule have a cost in sound and intonation.
There is also a notion that some instruments project in a way making them easier to hear. This can help match the expectations in our heads to what the trumpet actually sounds like. When we match instruments to our sound concept, they are easier to play.
