Yes, the rich have a burden to carry as believers, because there are many snares.
1 Tim 6:17-18 "Command those who are rich in this present age not to be haughty, nor to trust in uncertain riches but in the living God, who gives us richly all things to enjoy. 18 Let them do good, that they be rich in good works, ready to give, willing to share,"
However, there were a few rich believers, and they apparently managed to serve the Lord.
Phile 1:1-7 "Paul, a prisoner of Christ Jesus, and Timothy our brother, To Philemon our beloved friend and fellow laborer, 2 to the beloved Apphia, Archippus our fellow soldier, and to the church in your house: 3 Grace to you and peace from God our Father and the Lord Jesus Christ. 4 I thank my God, making mention of you always in my prayers, 5 hearing of your love and faith which you have toward the Lord Jesus and toward all the saints, 6 that the sharing of your faith may become effective by the acknowledgment of every good thing which is in you in Christ Jesus. 7 For we have great joy and consolation in your love, because the hearts of the saints have been refreshed by you, brother."
It is probably true that a large percentage of believers have come from the poor, but not all the poor have come! It is true that "not many" rich, etc. (1 Cor 1) have followed the Lord, but some have. The problem is covetousness, and I have known lots of poor folks with a covetous heart, and several rich folks with a heart bigger than their bank account, who loved the Lord in word and deed.
By the way, I am middle, middle.
Mat 27:57 "Now when evening had come, there came a rich man from Arimathea, named Joseph, who himself had also become a disciple of Jesus."
Acts 16:14 "Now a certain woman named Lydia heard us. She was a seller of purple from the city of Thyatira, who worshiped God. The Lord opened her heart to heed the things spoken by Paul."
Acts 16:15 And when she and her household were baptized, she begged us, saying, "If you have judged me to be faithful to the Lord, come to my house and stay." So she persuaded us.