Crazy idea. I had thought about it too, luckily discarded. Takes up a lot of space and is expensive. Every good gas grill already has a cooking surface, can be used almost all year round. Indoors induction and good pans.
There is one reason against induction: if you have a pacemaker. Then you should not stand in front of it. So if you also like to cook at the same time, an alternative would be good.
Well, an induction cooktop is not really a problem regarding pacemakers, at least not with normal use. Today's technology is very advanced, and much of what may have been borderline in the past is no longer an issue. At my previous workplace, a university hospital, there was a research group focused exactly on this, and I was responsible for the statistical analyses. They dealt with fields very different from those generated by an induction cooktop at normal distance. So you can be reassured.
Most things in our kitchens "aren't worth it" when you look at them rationally. But we don't do that. If you want gas for cooking, you just implement it. I wanted to as well. Would have needed bottles too. We know those from the gas grill and camper van. We then decided on the lower-maintenance option – so gas wasn't that important after all.