Thank you so much for your question and your openness to discussing a topic many would find very uncomfortable or flat-out offensive. I'm about to offend many people below. 😄

As you mentioned, the problem is not necessarily the accent itself. There are many people who would debate the things I say by posing edge cases (e.g. maybe you have a super thick accent but you have perfect vocabulary and you enunciate clearly so everybody understands exactly what you mean all the time). I think people who bring up those edge cases are ultimately trying to reduce their own discomfort with the fact that people with accents are, on average, simply harder to understand. I'll strengthen their case by saying it should be obvious to anyone that if we both worked in the UK, having a UK accent would make you far more intelligible than if we both worked in the US and you had a heavy Scottish accent. In fact, I had to work in the UK for nearly two years before I didn't struggle with understanding what many people said on a day-to-day basis.

To your core question about the opportunities people miss because of their accent: the friction it takes to work with someone with an accent reduces the opportunities they're given and the number of things that others voluntarily work with them on.

A concrete example from my own experience about two months ago is that I was asked to speak at a conference. During that conference, one of the sessions required someone to emcee and kick it off. At first, I wanted to yield the floor to another participant on the leadership panel because I was already giving a keynote at the conference. In truth, his accent was so thick that it made him hard to understand in many cases, and he was objectively not the right person to choose for the job.

I did not have the heart to say that; or perhaps, less charitably, what I would say is that I lacked the spine to actually just say the truth because I didn't want to offend him. A much more mature coworker of mine, however, stepped in and politely suggested that I instead emcee the session, which in the end was the best thing for the conference as a whole.

We were absolutely not trying to box him out based on some race-related thing or some national origin thing. It's just objectively true he would have done a less effective job leading the session. This, however, is the very type of thing that nearly no one will ever tell you to your face because they are so afraid of being judged by others. The need to virtue-signal great openness-of-mind prevents most people from telling you this truth: that accents create gristle or friction in working relationships which are obviated by choosing a different coworker.

Developing the right accent is difficult, but empirically possible, given evidence like the many actors who master speaking in different accents. I think the willingness to be deliberate about practicing different accents is essential. This was a huge difference between my mom and my dad, who both came to America at the same time and lived in the same house for the last 40 years. My mom was very interested in improving and did so measurably, simply by paying attention to it and taking opportunities to speak with her American coworkers. My dad took the opposite approach and had worse results.

I also suspect this is an area where professional coaching would help. Hiring the same type of coach that works with actors to produce accents (for instance, the type of coach that helps an Australian produce an American English accent) is almost definitely going to be more effective than just watching a lot of television on your own. This, of course, doesn't guarantee success, but I am shocked at the tremendously small number of people who are willing to invest even a few thousand dollars on their entire career future.

I think your openness to considering this area bodes very well for your success.