Okay you can have you papal electoral system but the casting of lots for Matthias was still a mistake that lead to all the denominational wars since then.
That is a non-sequitur. In no sense can you attribute any of the schisms of the church to the election of Matthias, which was entirely uncontroversial.
The first schism involved Simon Magus claiming to be an Apostle after having been shunned by St. Peter for attempting to buy his way into ordination.
Subsequent schisms involved Gnosticism, the denial of the humanity or the divinity of our Lord, et cetera.
The enduring schism between Catholicism and Orthodoxy dates from 1054, and in my opinion is primarily the result of meddling in the affairs of the Roman church by Charlemagne centuries earlier. The controversy between Catholics and Protestants exists largely as an overreaction to problems specific to the Roman church in the middle ages and early Renaissance, which never plagued the Eastern churches.
There are some schisms in the East, but no history of "denominational wars" on the scale of, say, the Wars of Religion of the 17th century.
And you cannot link any of this in any logical way to the election of St. Matthias. There is no demonstrable causal relationship.
In your zeal to attempt to find a culprit for problems in the Roman Catholic church, you managed to needlessly disparage St. Matthias, St. Peter and the other ten Disciples, and St. Luke, when in fact the Catholic church doesn't even use that system. I would urge you to retract your claim in the OP completely, since it rested on a false premise, and caused you to call into question the intelligence, moral character and godliness of the eleven good disciples, including St. John the Beloved Apostle and St. Matthew the Evangelist, in addition to that of St. Matthias the Apostle, and of St. Luke the Evangelist.
And by extension, you called into question St. Mark, since his successors in Alexandria were always chosen by the same system as St. Matthas.
So that is all four Evangelists, and all twelve Apostles, that you have effectively blamed for various problems specific to the Roman Catholic Church, which never happened elsewhere, and which they were in no respect culpable for (in particular, given that all of these problems of the RCC involved corrupt clergy ignoring the specific instructions from our Lord conveyed by the four Evangelists in their Gospels, and in Acts, and by St. Peter, Jude and John in their Epistles).