Oh, I feel honored that my comment had you look at it from an additional angle! Thank you.
(I started ̶w̶r̶i̶t̶i̶n̶g̶ ̶a̶ ̶r̶e̶s̶p̶o̶n̶s̶e̶ nerding out a little bit and then realized it might be helpful to add headlines. 😄)
Legal perspective
From a purely legal perspective, I’m not sure if it would make a difference to understand privacy as a “property right.”
Both property and privacy rights are not absolute
That is because many rights are not guaranteed unconditionally. Of course the situation varies from legal order to legal order but I would assume that in most place, this is both true for the right to privacy and to property.
Privacy right example:
So, let’s say X has a right to privacy but under certain conditions, law enforcement may be allowed to tap into his private phone conversation.
That’s because the right to privacy is typically not absolute.
Property right example:
Y has the right to have her house but if her house is posing a public danger (for instance, because the roof is about to fall off), public authorities may be allowed to force her to renovate that.
Again, that is because the right to property is not absolute, either (it is, for instance, subject to paying applicable taxes).
Universality of property and privacy rights
Unlike the right to property (which is not included), the right to privacy is guaranteed in the International Covenant on Civil and Political Rights:
Article 17
1. No one shall be subjected to arbitrary or unlawful interference with his privacy, family, home or correspondence, nor to unlawful attacks on his honour and reputation.
2. Everyone has the right to the protection of the law against such interference or attacks.
So from that perspective, privacy rights may actually be more universal.
Non-legal perspective
Of course, from a non-legal perspective, I think it can make a lot of sense to think of privacy as an asset. One advantage of that approach is that I think it could get people to take action to protect their asset.
That was fun to write, thanks for your question that got me thinking about this!