There are some medical reasons why they like you to get out although I am not too sure how much evidence there is to support them.
See this site for more info https://www.homebirth.org.uk/water.htm
'The other issues apply if you are planning a natural (physiological) third stage, but not if you intend to have drugs to speed up the delivery of the placenta. Some sources suggest that staying in the pool for the third stage can delay the delivery of the placenta and hence increase blood loss, particularly if the water is warm - 36-37C. There has been little research on this in the English-language literature on waterbirth, but in Germany apparently the practice is to have the pool at 35C or below for birth, and in 'Holistic Midwifery', Anne Frye states:
"Enning finds that uterus clamps down rapidly after a waterbirth, especially when the water is around 86F (30C), although colder water can lead to premature separation. Conversely, if the water is too warm, the placenta can be retained for hours." (Holistic Midwifery vol. on labour and birth, p479)
There are also concerns about the baby receiving too much blood through the cord after birth, if you remain in the pool and the cord is not cut - the idea is that the warm water keeps blood vessels dilated which would otherwise have closed down in a physiological (natural) third stage. If the baby receives too much blood in this way then it may become very jaundiced (neonatal polycythaemia) . Although there has been one case reported in the medical journals which may have been due to a third stage in water, this cannot be known for certain - after all, many babies have the same problem after land births, and managed third stages. It is certainly true that most babies have had no problems after third stages in water. It is possible that this is a theoretical concern rather than a realistic one.'