The uchihas Kekkai genkai goes more than just their sharingan, them awakening their eyes is just a bonus for the trials they went through. Besides the emotional issue, they worked to get those eyes.
What you have said can be true at times, but then there are other times where sharingan and associated powerups seem completely free.
For example:
Sasuke trained hard for years to kill Itachi and then finally killed him and awakened the mangekyou. That is an example of how an Uchiha can work for those eyes.
However on the flip side, you have Sarada who awakened sharingan just out of the excitement of seeing her daddy. That is an example of an instance where it seems free.
Also, one can make a certain argument about the whole emotions aspect of Uchiha eyes: There are many shinobi who experience just as much (if not more) pain than alot of these Uchihas. For example, Tsunade lost both her brother and her lover in very gruesome manners during war. Naruto lost Jiraiya, and Hashirama/Tobirama lost their brothers Kawarama and Itama during war at very young ages. As you can see, multiple shinobi such as these people have experienced the same trauma that would ultimately awaken sharingan or MS for an Uchiha, but these people did not awaken such eyes simply due to not having the right genes. Yet an Uchiha experiences the same type of trauma and goes from genin level to potentially kage level in an instant. Do you see how even the emotions aspect is still somewhat of a shortcut or an advantage for an Uchiha?
Over all, the eyes can be worked for, but they can also come relatively freely. It really just depends on the circumstances.