Riches can be one's real security is idolatry, or can be a hinderance to faith, and thus being rich is not to be one's real goal in life, and therefore the command to certain rich souls to divest themselves of their wealth .
However, the command to the rich by Paul in 1Tim 6 was not to divest themselves of all their wealth and live in poverty, but "that they be not highminded, nor trust in uncertain riches, but in the living God, who giveth us richly all things to enjoy; That they do good, that they be rich in good works, ready to distribute, willing to communicate [share];" (1 Timothy 6:17-18)
Being ready to share of their wealth out of a heart surrendered to Christ is not the same as divesting themselves of all their wealth and living in poverty. Yet it is hard for a rich man as a rich man to enter the kingdom of God, due to the false security and selfishness that usually genders, which is contrary to salvific faith. But with God all things are possible.
And as said, it is not by literally leaving all that one gains eternal life, but by having saving faith which is characterized by obedience, forsaking all in heart being part of that, (Lk. 14:33) and the resultant works of faith are rewarded in grace in addition to the gift of eternal life.
Not necessarily, -- I agree with the rest of your post. Monastic life is not indeed the only vocation that can lead to salvation, but it is an important one, and in America shaped by Calvinism it is especially important to underscorethe salvific quality of religious dedicated life, for every American need to recognize himself in the young rich man of the Gospel.