Phrases like "hold on to" and "let it go" are vague. It's not up to me whether or not I experienced something in the past. I could no more choose to hold on to an experience than I could choose to let it go. What I can do is study it to understand how it made me feel, what those feelings mean, and so on.
I think when the voluntary phrase "hold on to" is used, it's meant to refer to the involuntary experience of not being able to think of something other than what's being "held on to." This would be an indication that the person has not studied it to understand how it makes them feel, what those feelings mean, and so on. Their subconscious preoccupation is an indication that it needs processing. To "let it go" would be very unhealthy.
If you drive your car into a brick wall, you need to remember how it felt and the property damage that was caused to you, your car, the brick wall. Otherwise, what's stopping you from doing it again? Our ability to remember our experiences and especially the processing of the traumatic experiences saves us both from being subjected to those experiences in the future as well as subjecting others to similar experiences because of us.
It's not just for the traumatic either. If we find ourselves the beneficiaries of a very satisfying experience, to process it will help us understand how to achieve satisfaction in the future as well as provide satisfaction for others. There is no flaw in allowing knowledge (and experiences if we have self-knowledge) to accumulate and improve who we are overall.