I went with a private tour guide and my husband. We did go into the cave. In my experience, there was no chair/ladder assistance as there sometimes is (according to online reviews I have seen) so we just jumped down a hole into the cave and had to climb out. As a reasonably fit athlete in my 20's I still found the climb out fairly challenging (you essentially need to do a pull up of your full body weight while holding on to uneven and sometimes wet lava rock). I 100% see why so many people get stuck. I would strongly caution anyone against going alone, going if you do not have a good understanding of the tides, or going if you or those with you are not in good fitness.
For what it is worth, I don't feel a need to do it again. Very much a one and done thing. I don't think it is a must do.