There is no reason why an epidural will increase the likelihood of a Caesarean section delivery.
The most common indications for emergency Caesarean section delivery in labour are lack of progress in labour (cephalo-pelvic disproportion or the baby is too big for the birth canal) and foetal distress in labour.
Sometimes there can be a brief episode of foetal distress immediately after an epidural is sited because of a fall in maternal blood pressure. But with correct management, this can be corrected (intravenous fluids and correct positioning on your side). This risk can be minimised with preloading (before the epidural is sited) the patient with intravenous fluids
I agree there is an increased risk of an operative vaginal delivery with an epidural working. This is because you don’t have that incredible desire to bear down in second stage labour, and so pushing is often not as effective or as strong. Also you are not sure about correct direction for pushing.
The increased risk of an operative vaginal delivery (vacuum or forecps delivery) can be minimised by waiting in second stage until the baby’s head is very low in the pelvis before you start pushing, so you are not pushing too long and don’t get too tired. Also the risk can also be minimised by allowing the epidural to start to wear off, so you get some sensation back. But many women don’t want this option
For the same reason an epidural is associated with a greater likelihood of an intact perineum and if there is perineal tearing a less severe tear. This is because you do not have that incredibly strong desire to push and so there can be a slower and more controlled delivery of the baby’s head, with a more controlled and gradual stretch of the vaginal entrance.