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I think this did not address what I think is the key part of the question which is 'how can something have an intrinsic value if value is subjective'.

I simply do not think all value is subjective. One can alter value through their own subjective experience. I personally still hold on to a paper napkin from a sentimental trip that I went on, and that creates a personal premium value for that napkin that goes above the utility and scarcity conditions of that napkin's value.

The contrary is obviously true. I doubt there are many monks that intend on buying Ferraris, even if they had the means to do so, so their subjective value impacts what would be considered the total of a Ferrari.

However, to speak of the 'intrinsic' side. I think value is best split into a multiplicative relationship between utility and scarcity. A toll road is a great example. Many times, there aren't many alternative roads, if any, and its utility at getting you to where you need to go should be non-zero assuming you intend on going where that road takes you. So, if a toll road were to crop up on the market selling for $1 dollar, assuming no 'strings attached', that would be a clear mispricing one could diagnose on an 'intrinsic value basis'.

I think it's incorrect to say that something cannot be intrinsically valued due to subjectivity being the primary motivator for humans, and so since subjectivity drives exchange, valuing that relationship is not possible. We can have long lasting theories of human behaviour or social systems that allow us to assign an objective/intrinsic value.