Why are Goten and Trunks able to go Super so easily while Goku and Vegeta had to struggle to reach these forms? Do they hurt the legacy of the form? I'm gonna explain some of my reasoning here.
The Super Saiyan form is attained through experiencing intense rage and hatred. This happens to Goku after witnessing Krillin die and Vegeta becomes. Infuriated with himself for not being able to achieve the form that Goku did. So how could carefree children also achieve this form??
I'd say they're not carefree. Goten and Trunks are both little kids who go through high and low emotions all the time. A child can't control their emotions very well so I say it wouldn't take much to achieve the proper amount of anger.
Why didn't Goku transform after Krillin's first death in the original Dragon Ball series?? I say... He simply wasn't strong enough! To achieve Super Saiyan I believe the requirements are you have to be up to a certain level of strength and experience the pure rage I talked about above. Young Goku simply wasn't strong to attain the form. So they may take away from the legacy of the form a bit as they are children who achieve it pretty easily. However, I feels it fits the rules for achieving the form well and actually makes sense.
Tell me what you think about the transformation and how it works in the comments below. Have a great day! Ja ne