Turbo engines use massive amounts of fuel and oil under boost. A fuel efficient Na motor will get better fuel economy out in the real world than your average turbocharged motor 9 out of 10 times. Turbos are not efficient the way the average driver would use it...
Rotaries are a pretty good design. Very smooth and free revving, I liked the power delivery far better than the Subaru brz I drove. It felt quite fast in the higher rpms.
Rotaries are actually a relatively decent engine, but no one knew how to take care of them coming from a piston engine so they were failing left right and centre. I've seen some last when taken care of properly.
Now, using Mazda's rotary phase to judge the brands reliability as a whole? Ridiculous. They got some of the best piston engine designs coming out of Japan for decades now, even Toyota took notic right after Ford.