Do media interviews enhance or potentially spoil academic reputations
The simple answer is that it depends on in what context the appearance occurs.

If you become visible as an expert in your field your appearances will build your reputation among the public as an expert. As such you will gain a positive (trustworthy) reputation which I am sure will be seen as positive in many respects. The university will gain credit by having employees appear as experts In my country all faculty also are mandated to convey science to the general public and appearances in media is one way to do this. So my guess is that the department and the university as well s your own discipline will see this as beneficial.

Obviously, if you appear with politically incorrect views it will all be negative. Another problem that I am sure will appear is jealousy from colleagues who do not appear in media. In the end your success depends on how you get portrayed in the media. My university runs media training to ensure that faculty represent the university in an appropriate way.

In the end positive media visibility is not likely to strongly affect your research career in terms increased funding, the systems should not really be influenced by it but we all al human. Media visibility will mainly affect the way you, your discipline, the university etc. is perceived by the public. It may, for example, influence the way politicians distribute research funding.

So, media interviews can potentially both enhance or spoil a career depending on the context in which you appear. I believe it is important to know how media works and universities often have programs (and sometimes also rules) to help in such contacts. Depending on the type of question to which you are requested to respond you need to be able to assess how answers will be used or perceived. If the interviews are on non-controversial topics, it is probably not problematic but if you are approached on a burning issue, be aware and be savy