We never did it for our first few years together, mainly because we went to different dentists, different GP surgeries, as we worked and lived in different towns.
Over time, we've morphed into going together because it's more practical now that we live and work in the same place and have moved GP surgeries, dentists, opticians, pharmacies, etc., to the same ones, closer to home.
Now we basically go to virtually everything together, i.e. one journey, one car park charge. It's also easier to make "joint" appointments, i.e. one phone call to make appointments for us both at the same time, rather than having to phone separately at different times of the year, etc., especially when GP surgeries and dentists make it so hard to contact them by never answering the phone, not listening to answerphone messages etc (our dentists are terrible for that!).
Just booked for our flu jabs (together) next week and covid jabs (together) the week after, and our dentist appointments (together) in December. And yes, we do go into the surgery/treatment room together, but that's more because DH has had cancer for 8 years and needs help with him being unsteady on his feet due to the side effects of the chemo.
We also got into hospital/consultant appointments together because there's often a lot to talk about and things are easy to forget (i.e. forget to ask the consultant or forget what the consultant has said), so by going in together, one of us will remember if the other doesn't.