Yes, it is much the same for me, but you can register at other specialist government hospitals if you need. I'm registered at the local town hospital, 2 public hospitals in Mahasarakham and 2 in Khon Kaen.
Yes, the wait times can be long, but if you get referred to a specialist you can normally get an appointment to see them within a week. If you have regular apointments, you can usually suss out the best time to turn up. For example, I have a regular, 3 monthly appointment for the eye doctor. She normally see over 100 patients and most Thais turn up early. I usually turn up abut 3:00 pm, when most people have gone and don't have to wait long.
Yes, meds are free through the public hospital system. I currently have three different bottles of eye drops per month (you get 3 months worth at a time at the hospital pharmacy). The subsidised cost in Australia is equivalent to 2,500 Baht per month for the medications, plus about 5,000 Baht co-payment for the doctor visit every 3 months. Here it is all free.
I also have private insurance in Thailand, but I recently turned 65. The premium doubled from 25,000 per year to 50,000 Baht. I'm yet to use that insurance, but will keep paying the premium as long as I can afford it.