Anglican ceremonies at least have to be conducted in a church (not so in every country and denomination). If you want to be married outside a church, you can only have a civil wedding. But then you would have if you chose a blessing performed by a priest after.
There are also strict regulations about where you can hold a civil ceremony in the UK. Was one if the reasons Charles had to have it at registry office.
The royals tend to have religious weddings because of their role in the church. Even minor royals stick to that. Further from the throne, as civil weddings become more common, we may see that change as time goes on. But close to the throne, like Harry, no.
Edward and Charles are not true examples. Edward was marrying a twjce divorced woman which was not allowed. While Charles could have married Camilla in the church as rules changed, it was decided against. Since Camilla had a place in the break up if his first marriage, it would have been seen by many as special treatment for him. And for thevfuturevgeae if the church, it wasn't seen as sending the right message.