Well I would argue this is the teacher student phenomenon. You remember your teachers from school, for example, because you saw one teacher per subject per year. The teacher may not remember you, because they saw hundreds of students per subject per year. The hosts are in a similar position… there are thousands of people who may watch an episode and feel a connection to one host, but there is no way that the host can have a meaningful connection with thousands of people.
On the other hand, if you are offering them something useful, say content for a show, you could share that… but then you’d need to expect that content not to remain private if it were to be used on a show.
I don’t think they’d disdain a pleasant interaction, but I think it just boils down to “who has the time” when they’re busy moving on from yesterday’s work to planning tomorrows content.