I would liken mouthpiece, instrument, and player, to car and driver.
A new or inexperienced driver does not have the skills or experience to benefit from driving different cars. They desire a change to drive faster or better but they cannot fully extract higher performance from the cars they drive.
A seasoned driver with huge experience understands the car and their abilities far better and they know how to extract good performance from the car and they can successfully change vehicles and extract high performance from each one they change to.
In other words the seasoned professional can acclimate quickly to a new car, when the inexperienced driver cannot.
I cannot speak for other players but my personal experience is I can now acclimate quickly to a new mouthpiece or new instrument, where before when I was far less experienced, it took me a long time to acclimate following a change.
I also believe that failed mouthpiece safaris may be at least partly due to the player embarking upon the safari at a point in their playing when they are less able to benefit from the changes in the safari.
I have myself never gone on a safari, I have known there is a problem, and known what mouthpiece size and shape is likely to help resolve the problem and then made a change to see if I am right. Usually I have been right.
Having a collection helps me in doing this.
Knowing your playing, knowing your equipment and knowing what effect the change will make goes a long way to making the right choice when changing and having a collection enables test changes to happen easily instead of having to wait to acquire a test mouthpiece you do not possess.
It was obvious to me just as soon as the wick 4 that I use now was in the breech, that it was the right choice partly because I knew before trying it that it was more than likely going to resolve my issue at the time and why it would resolve it.
No acclimation was needed. It has been good from the first note and has since performed faultlessly for several months and for hundreds of performances in all styles from salsa to blues to jazz to legit to baroque and to opera.
Know yourself, know your equipment, know what difference a change will make then there is a good chance the change will take you at least part of the way on your journey.
Like a journey from arizona to washington, knowing where you are, knowing where you need to be, and having a good map, helps to get where you need to be and helps stop you getting lost on the way.