Those types of welders are out there but they tend to be prohibitively expensive, for the best all round I would stick with the Mig welder. As a qualified Arc welder I can tell you there is not much you cannot do with a decent Mig unit. Tig welding produces a beautiful product but it is also somewhat of an art and can be difficult to master.
Now I need to start looking at them. I want one that will be good for learning, but also last me for a long time to come, especially if I get more into it.
I’m hesitant to buy a HF welder for example.