According to at least one source, Achilles, the hero of the Greeks in the Trojan War, was said to have been made invulnerable when his mother, Thetis, dipped him in the Styx, the great river of the Underworld, immersing all but the heel by which she held him. From this we are given the expression the "Achilles Heel", which implies that something is not only a source of weakness, but that the cause of the weakness is also the source of great strength.
Agile has an Achilles Heel: the Product Owner. The involvement of an empowered, knowledgeable, committed and engaged Product Owner is a source of tremendous strength and benefit of the agile approach; in fact, the Product Owner is the single indispensable person on the project, without whom nothing can be done. Like Achilles, the Product Owner seems to need to have powers beyond that of mortals: they must negotiate consensus with all the stakeholders in the business, they need to be almost omniscient in their knowledge of the business domain and the goals of the project, and they must be unfailing in their vision of the solution to be developed. Oh yes, they also need to be available any time the development team needs them for feedback. When presented in these terms, the Product Owner seems just as mythical a being as Achilles himself.
The reality, on real projects, is that it is almost impossible for one person to do all these things well. If the Product Owner is a skilled negotiator of consensus among stakeholders they are not going to be in the team room all the time. If they have a strong vision for the solution that vision is likely needed elsewhere as well. Visionaries also sometimes have a great "global view" but are sketchy on important details. If they don't have a compelling vision for the solution they may vacillate or even flip-flop on important decisions. If they lack important negotiating skills they may tell the team one thing only to have their decisions overruled later by stakeholders who were not involved.
The reality is that there is often no one person who can fill all the roles the Product Owner must fill. In these cases you will have to find different people to play different aspects of the Product Owner role. The best Product Owner is probably one who can negotiate consensus, make effective and timely decisions based on that consensus, and be available on a predictable basis to work with the team (though not all the time). When she lacks understanding of the details of how something should work, she will enlist the support of the right people and get them engaged as needed. The grand vision is important but as long as it is provided by one of the stakeholders the Product Owner need not be the "big picture visionary".
The most important thing the Product Owner can provide the team is consistency, in participation, and in direction. If she can do that, she need not be some mythical hero. As long as the right people can be engaged at the right time, and as long as the guidance provided by the Product Owner accurately reflects the desires of the stakeholders and does not fluctuate over time, the agile team can make great progress toward delivering a solution that meets the needs of the business.