The beauty of Yeshua’s teaching here is easily lost through a number of false assumptions:
(1) Yeshua’s main concern is where people will dwell in the life to come
(2) Yeshua teaches that few will ultimately find a good afterlife
(3) Destruction and life are terms referring primarily to the afterlife

Each of these assumptions can be shown false.

First, in the overall tenor of Yeshua’s teaching, the concern is as much about this life as the life to come. Not shying away from strong teaching about the life to come, nonetheless, Yeshua speaks often of kingdom realities now, discipleship in the present, and abundant life now and not merely in the life to come. Furthermore, the immediate context of Matthew 7:13-14 is discipleship in this life:
…7:1-5, Avoiding an overcritical spirit
…7:6, Avoiding a naive spirit
…7:7-11, Trusting God for good things
…7:12, The Golden Rule
…7:13-14, The narrow and wide roads
…7:15-20, Good and bad fruit
…7:21-23, The claimers and the knowers
…7:24-27, The house on sand and the house on bedrock

Second, Yeshua does not picture God’s redemptive love as being limited to a few or inclusion in God’s kingdom as an elite accomplishment of the few. Far from it, Yeshua proclaims hope for unimportant people, the poor and downtrodden, the masses. His descriptions of God’s redemptive love picture the gentiles coming to faith. He opposes the elitist strain of Israel’s current leaders (priests, Sadducees, aristocrats, scribes, Pharisees). He deliberately describes many being in the kingdom:
…I tell you, many will come from the east and west to share the banquet with Abraham, Isaac, and Jacob in the kingdom of heaven (8:11).
…the Son of Man did not come to be served but to serve, and to give his life as a ransom for many (20:28).
…Blessed are the poor in spirit, for the kingdom of heaven belongs to them (5:3).
…For my yoke is easy to bear, and my load is not hard to carry (11:30).
…look up and see that the fields are already white for harvest! (John 4:35).

Many other sayings of Yeshua speak of many downtrodden people being called to God’s banquet, God rejoicing at finding and redeeming sinners, of unrighteous people finding God’s forgiveness, of Yeshua as the physician for sin-sick souls, of his seeking and saving the lost, as the shepherd bringing in many sheep into the fold, and so on.

Third, in keeping with wisdom teaching such as the book of Proverbs, and Yeshua’s teaching often relates to the wisdom literature of the BIble, life and destruction are descriptions of conditions in this life. People are destroyed when they lose all peace and choose the seductive path of immediate success and gratification. Their lives wind up empty and filled with pain. But those who choose the harder path of discipline, submission to correction, learning wisdom, and choosing the fear of heaven find abundant life. (See below for an appendix, “Life and Destruction in Apocalyptic.”)

In context, Yeshua’s saying about the wide and narrow road is about those few who find and practice wisdom, discipleship, and specifically Yeshua’s teaching in this life. It is not about God limiting redemption to the few who find and follow such a path. If we want to discuss the limits of God’s saving and who will be redeemed and who will not, we simply will have to look to other biblical passages (or, perhaps we will find that ultimately the question is not answered with any specificity in the Bible).

The call to follow Yeshua’s teaching is not about our final destiny, but about knowing life, joy, peace, wisdom, responsibility, discipline, and the hard, but rewarding, work of love in this life. Few will follow this path. But Yeshua defines it as true life and the broad path of self-service, substitute joys, and empty gratification is really destruction.
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APPENDIX: Life and Destruction in Apocalyptic
There is no denying that Yeshua was an apocalyptic teacher. And in apocalyptic writing (a Jewish genre which was heavily used shortly before, during, and after Yeshua’s time) there is plenty of language about final destinies in heaven and hell. This could be the background of Yeshua’s saying instead of assuming the wisdom literature of the Bible is the background.

Dale Allison notes that in apocalyptic writing, the idea that few will ultimately be saved is expressed in some places (4 Ezra 7:47-51; 2 Baruch 48:43).

However, the context of Matthew 7:13-14 is much more wisdom literature than apocalyptic. Warnings against being overcritical, wisdom to discern people based on good fruit or bad fruit, and talk of building one’s life on the teachings of Yeshua in order to build the house (of wisdom, a common image in Proverbs and Psalms) puts the language in the realm of wisdom.

And wisdom literature uses terms like life and destruction in the sense of this life. Examples include:
…Proverbs 2:18-19, the adulteress leads people away from life toward death.
…Proverbs 2:20-22, two ways lead either to living in the land or being cut off, torn away.
…Proverbs 3:2, wisdom leads to life and abundance.
…Proverbs 4:22, the teachings of wisdom are life to those who find them.
…Proverbs 5:6, the ways of the adulteress are not straight on the path of life.
…Proverbs 7:2, keep my commandments and live.
…Proverbs 8:35, whoever finds me finds life.
…Proverbs 14:11, the household of the wicked will be destroyed.
…Proverbs 15:11, death [Sheol] and destruction [Abaddon] are before the Lord.