Absolutely yes. But you have to do this either way. So it's just purely additive work to run the infrastructure as well.

I think if it were true that the tuning is easier if you run the infrastructure yourself, then this would be a good point. But in my experience, this isn't the case for a couple reasons. First of all, the majority of tuning wins (indexes, etc.) are not on the infrastructure side, so it's not a big win to run it yourself. But then also, the professionals working at a managed DB vendor are better at doing the kind of tuning that is useful on the infra side.