Worked for me on the second try.
Not sure exactly what the difference is with it working and not for some people.
I tried this several times (luckily I have a friend with more credits than they know what to do with, so doesn't mind buying a cheap 2 seater and blowing it up for science) and I always ended up back in the taxi, circling forever. I'm newish to the game, so I hadn't really accomplished anything (handful of completed missions, around 2.5 million credits) so my workaround for this was to just delete my character and start over. It's unbelievable that the game was released with a bug like this, but so far my solution on the new character has just been to inspect the planet I'm flying to before using the taxi. If it has rings, I suck it up and fly my own ship. So far so good, besides occasionally crashing into the sides of space stations or other ships waiting in queue, Apex has been working fine.