Duct tape would add rotating mass without offering much puncture resistance.
There are proprietary products alleged to be designed to add a puncture proof layer. I haven't tried one of these since the 1980s because it was fiddly and ineffective. They may have improved in the >30 years since.
I went through a phase of having 1 or 2 punctures every 2 or 3 short rides. I was riding a mixture of roads and rough farm tracks, picking up thorns or getting snakebite pinch flats. I was running cheap original equipment 23mm tyres. I then bought 25 mm Continental Gatorskins and ride the same rough tracks faster and less cautiously and can't remember the last time I had a puncture.
I also have Gatorskins (28mm) on my gravel bike with similar success, and years ago I had one on my 700c unicycle which I usually rode off road and punctures were never a problem.
No doubt other brands are as good, maybe better, but point is that there are tyres out there designed to give you a fast and comfortable ride whilst being very resistant to punctures.
Tyres, pedals, seat: the three best upgrades for any bike. (Well, the 5 best, if you count both tyres and both pedals, but you know what I mean.)