Absolutely worth it in my book!
I had to have my gallbladder out after I got a gallstone stuck (it passed before I saw a doctor) and I got to choose my own surgeon and the surgery was done in 10 days and I got to stay in for 48 hours (which I needed). If I'd gone public I could have waited a long time, had my surgery time/date changed which would have stuffed up my work/etc and might have landed me in hospital with another stuck gallstone.
My dh broke his finger & needed elective surgery a few months later to fix an underlying issue. We got to choose a good surgeon of our choice and a date of our choice, which was important cause I was pregnant and the last thing we wanted was having his hand out of action when I had a newborn. If we'd gone public he would have been classed as non-urgent and could have waited 1 - 2 years for the surgery and yet be given a few days (maybe a few weeks) of warning of when it was going to happen with no choice of moving it if it didn't suit (eg. my due date for my pregnancy).
And my ds needed grommets at 14 months. We saw the surgeon at 5pm on a Friday and he had them on Monday morning. If we'd waited to go publicly he could have easily waited 6 months and his speech was already borderline (but the hearing tests were only showing slight impairment). If we'd gone public he could have ended up with lots more ear infections and a speech delay that would need speech therapy. We had neither. Instead we had a child that spoke well and most importantly started sleeping well as his ears no longer hurt at night!