1 Nephi 1:15
And after this manner was the language of my father in the praising of his God; for his soul did rejoice, and his whole heart was filled, because of the things which he had seen, yea, which the Lord had shown unto him.
After this manner... this tells me Nephi is somewhat paraphrasing, and there were likely LOTS more to the praising that what was contained in verse 14. His soul did rejoice, and when one's soul rejoices, there is a lot more than words that come out of their mouths. Lehi was joyous, thrilled, happy. His whole heart was filled, not just part. It wasn't bittersweet, but he found joy at what the Lord had shown unto him. This is not only a good reason to ask the Lord to permit me/you to have these experiences, but to earnestly get my/your life in order to be prepared for such things. Perhaps God will not grant us all these types of experiences, but James 1:5 says that God gives liberally to all who ask in faith. So why not ask in faith, and begin the process? It is possible.
Imagine if the whole world began this process, doing what it takes to turn fully to Him, and to experience such joy. This joy was resultant from a vision. Imagine what greater joy God can bestow upon us, outside of visions.