Yes they should tow you to your preferred repairer, unless your membership restricts you to a certain radius. My membership is for a 20km radius so if I'm 50km away from home, I get a free tow for 20km then have to pay for the rest of the way. NRMA won't change my tire for me because I don't carry a spare (
) or fix the puncture - that's a DIY job.
My issue with the free tow is the timing and cost. What do you do if it's a week night, Saturday night or Sunday when you get your flat tire? Even if you get your scooter towed to the repairer, you'll have to leave it there overnight until they open the next day. I was lucky with my puncture because it was in the middle of the tread and could be repaired with a plug. If I get the scooter towed home via NRMA, I can't call them out the next day to tow me to the scooter shop for free. They treat that as part of the original tow, and I have to pay for the tow. So, all up, I'd rather plug the tire if I can, ride it home so I don't worry about leaving it outside the scooter shop and ride it there the next day when they're open.
My understanding is that the puncture repair kit is meant to be temporary only and is to get you to a repairer. Having said that, the plug that I used was good enough to last a week until I could get the tire repaired....and I've heard of people riding thousands of kms until the tire needed repairing. It's really the inspection of the tire inside which is important....you don't know if there's a tear that'll get worse inside the tire even if you plugged it. The repairer will fit a permanent plug from the inside of the tire and it should be safe. If not, you're up for a new tire. I think legally, you can only have 2 plugs (temporary or professionally fitted)....after that, time for a new tire. If it's a sidewall puncture, again, it's time for a new tire....you can't plug those.