There are ways to ensure the correct transfer of ownership without involving a third party. You can see these principles at work on some trading platforms already, be it for Magic cards or something else where parties cannot trust each other because they do not know each other.

Next, you would expect that the notary would educate participants and act as a source of trust, an actor in your best interest, but that is not the case. Notaries can change contracts until the last minute, and unless agreed upon, the common 14-day withdrawal period for contracts does not apply to things like buying property. Furthermore, if you are inexperienced, you can easily fall into traps.

As a concrete example, when buying a part of a shared property, it is commonly believed that the "Hausordnung" (house rules) is the owners' agreement for house rules. However, that is not the case, as there can be more, and in our case, it forbade us to keep dogs. Now, you could argue that we should have made ourselves more familiar with the law, and I would agree that is true. However, it begs the question, why do we need a notary?