for what purpose do Catholic Churches have statues of Saints?

Statues ( or icons in the Eastern Christian tradition ) are an aid to veneration of the saints and a means of remembrance of the heroes of the faith.

None of this is in opposition to God. St Jerome said that "we show veneration to the servants so that it might radiate back from them to the Lord."

No Catholic who knows anything about the Catholic faith has ever worshipped a statue of plaster (as in pagan idolatry). Devotion to saints no more interferes with or corrupts the unique adoration due to God than does love for our friends and relatives.

If we cherish the memory of mere political heroes such as Thomas Jefferson with statues, and war heroes with monuments, and even great sports figures (e.g., statues of Michael Jordan in Chicago or Joe Louis in Detroit), then what can be the objection to honoring saints and righteous men and women (Rom. 12:10; Heb 12:22-23; 1 PT 2:17)?

The Bible says we are "surrounded" by "so great a cloud of witnesses" (Heb 12:1). These are the saints in Heaven.

many commentators think this vivid metaphor is describing the saints in heaven watching us and cheering on us on, like spectators in a sports arena. Catholics also believe in angels, and guardian angels for each person, as indicated in biblical passages.