Very, very good question. The kind of question that made me have to rethink my own beliefs on the subject. I'd like to ask you to define intuition though, just to make this clear. By the way I have never come across this question or anything like that, I'm just going based on my own readings in phenomenology and existentialism. Let me give an example of how I see it to try and flesh out the possibilities in this discussion:
Say you're making bread and decide to knead it. The process of interacting with that object, of knowing when it is right to stop, of imagining the different possibilities of the bread, of the different textures and weight etc. Isn't that a kind of intuition? What about when you play an instrument that you have never played before, feeling your way around it isn't a matter of reason, but a kind of intentional attachment of your own consciousness onto the object.
Let me also blur this a little further. Don't we often treat people, ie subjects, as objects? If you are a traffic warden and you control the flow of traffic with intricate hand signals, you are almost playing a game. On some abstract level we know we are dealing with thinking subjects, but at that moment it is not the main point and rarely surfaces unless something goes wrong. The point is to succeed in getting cars where the need to go as quick as possible. Don't we even objectify ourselves? For example, I'm applying to do a law degree, if I have to go to an interview, I will conduct myself as I imagine a good "person-going-to-a-law-degree-interview" would do. I'd dress nicely, not smoke beforehand, keep a good posture, pretend to be interested etc. We see ourselves as others would see us as objects, mainly the "person applying for law" object.
In this sense, I'd question 2 assumptions in your statement:
1. Can't we have an intuitional relationship with objects? Such as art, cooking, instruments etc. ie, aren't our relations with objects often subjective?
2. Don't we often treat others as if they are not really others at all, but simply components of this world like coins, bass lines and resignation letters? Aren't our "interpersonal relations" often objective relations?
Again, great question and I'd love to hear your views on the topic, especially if I've misinterpreted the meaning of your statement.