Thank you for this helpful observation. I agree...a common mistake is to fight (push forcefully away) intrusive thoughts. Calm acknowledgment before focusing the mind elsewhere is the key. Something like "yes, I am feeling scared, angry, hopeless etc..at the moment" but now I want to be elsewhere, do something else.
Other reasons why people reject mindfulness as "not for them" is because they only give it a go when the going gets tough. As I often point out, a competition, exam, sport match are not the time to practice our moves...Regular training when not under pressure does it.
Also, mindfulness doesn't come easy, because of the mind being allowed to run uncontrolled over a lifetime. Instead of being our mind, it becomes the tyrant that rules us. Old entrenched patterns do not disappear overnight...so many people give up, deciding it doesn't work.
When it becomes effortless habit, mindfulness has long-term, positive effects over all areas of Life.
Happy, peaceful trails to you, Traveller.