The idea of a special table for pregnant women is great in theory, the problem lies in the practice. The reason that you shouldn't sleep on your belly is so that your intrauterine pressure stays at a safe level. Granted, putting your belly through the hole doesn't increase the pressure on your baby, but it puts your ligaments at risk.
During pregnancy you have very different hormone levels. Relaxin in particular makes it so that your joints can shift and stretch without much pain. The problem is that you may not notice if your ligaments are getting strained. Your uterus is held in place by 3 sets of ligaments, and when you dangle your belly through the hole on the table, everything inside of it is pulling on these ligaments. That is the weight of your baby, the placenta, the amniotic fluid, as well as your other organs. Gravity is pulling your belly downward, and likely causing unnecessary strain on your ligaments. Some of these table come with a sling that is tightened under the belly to provide support for the ligaments, and many places that use these tables will say that it is a great solution to the problem. Unfortunately, if the sling is tightened enough that it provides support to your ligaments, it is likely to increase the intrauterine pressure and put your baby at risk, which is what you were trying to avoid in the first place by not lying on your belly.
Most people go to a massage therapist to relieve stress, and a major manifestation of stress for a lot of people is back pain. While you may not notice it as much when you are pregnant, using the belly holes on these tables can actually cause injury to your back. What happens is, your back isn't very supported and you have someone pushing on it. This unsupported pressure on your back can cause strain to the ligaments between your vertebrae, and due to the relaxin, you may not notice right away and some real damage can be done before you do.
These tables also don't adjust very well. There is just a single hole that you put your belly through that is supposed to be designed for all women in all stages of pregnancy. We all know that women come in all shapes and sizes, and even pregnant bellies come in all shapes and sizes. So, if a table is designed to fit a woman who is 5' 6" and you are 5' 2", you can see how your belly might not be in the same place as the 5' 6" woman, which means that it won't fit you correctly. If you are 5 months pregnant, and the table is designed to fit women up to 9 months, your belly is most likely going to be too small to fit well even if it does fall at just the right place on the table.