Also, the tubes for the individual valves have their own tuning slides. A trumpet will typically have a little thumb-operated lever for one of those slides, to help with some of the notes. I saw a video of a tuba solo, and the tubist was working the tuning slides almost as much as the valves.
Thumb-operated levers on trumpets are uncommon (though, IMHO ergonomically superior). More common are a ring in which you place your left ring finger. The ring is directly attached to a slide on the third valve, so you can flatten notes by extending your left ring finger.
Those removable slides are usually just to get the spit out of the loops. I haven't seen the lever you mention - are you sure you are not just looking at the usual [water key](https://www.youtube.com/watch?v=vMbb8-WK_VM)?
With valved brass instruments you are trying to approximate a logarithmic relationship with a linear sum of components. Trumpets have a high resonant Q, so not using the valve slides is going to produce out of tune notes. I played horn once upon a time. Horns have low resonant Q, so you just “lip it in”.
