I believe that one has to dress for one's part. Do you want to be seen as a doctor? Dress like a doctor. Do you want to be seen as a tech? Dress like a tech.
The easy way to decide is to look at how private surgeons dress in your neighborhood. If they wear suit and tie, the minimum for you is business casual. If they come to work in flip-flops, there is no reason for you to dress up. Except that you need to know that, especially in smaller places where everybody knows everybody, you are being judged also by the way you look coming to work. It's just human nature. People tend to be more respectful of well-dressed people.
A white coat helps, too. Yes, there are many non-medical people wearing it nowadays, even in my hospital. But when I wear that white coat that says MD and Critical Care over my ICU scrubs, people who don't know me need to take just a look to know that the viceroy is there. Definitely more respect than when I wear just my scrubs, despite the badge saying the same thing as the inscription on the coat.
If you have ever seen a scrub nurse or tech dressed well while coming from work you will get my point. It can change your opinion about them. Human nature.
The investment is just a few hundred dollars/year, but it will pay back big time. Don't forget that your bosses are also people. Would you go see your department chair in jeans, scrubs or flip-flops? I wouldn't. The important people tend to spend their days in meetings with other well-dressed important people, so they will notice if you are underdressed for the part.