There's limits to how much you can manage having your cake and eating it too. You're spot-on as far as changing the tune for street and track. Every additional horsepower adds stress on almost every component of your car; and while some parts might be robust enough to handle a good deal more power than stock, all you need is one part to be overtaxed to leave you stuck on the side of the road. Track use might put the same stress, if not more, on the rest of the car, but it's for a much shorter duration. But still, as you've probably witnessed, many cars blow engines and drive-trains at the track. Running a softer tune on the street mitigates much of this. Doing so also also allows for running more streetable tires when you're not on the track.
PLUS, as already noted, while bigger turbos can produce much more power, they also take longer to spool up, which can be a PITA when tooling around town. But only you can determine if a good stage 2 tune makes sense for your purposes, or if you really need to run a bigger turbo and tune, with the associated liabilities.