Partially managed for us, but it differs on the customer.
If a customer has no IT background, self managing is not an option.
If a customers main INCOME is from the website he runs ( Eg. let's say its a review site, or an online store etc ), that generates several thousands or more per month, it would make sense paying a few hundred or more for a fully managed service that mantains his server and ensures that its up for as much as possible so he can earn more money.
Furthermore, self managed -> an issue causing downtime -> Need to fix it asap, doesn't matter if you're asleep, on holidays or busy with family etc.
Managed solutions -> downtime -> open ticket -> continue sleeping/holiday/family time ( and periodically check the status of the site )