Wouldn't it? Given limitless energy, you can literally create matter out of thin air (E=mc^2) ...
You could create new planets, replicas of anything, etc. Hell, you could even distort time to fit your needs.
Granted, it would take more energy than exists in the universe - and a little technology that we haven't tried outside the lab yet. But we already have the fundamental tech to make that happen - it would just take a bit more scaling up and fine tuning.
Yes I think you are right. Solve energy, most other problems will the solved from that. (the only thing holding back would be the side effects or fear of the side effects of accessing that energy).
Even inventing a limitless supply of free energy would not eliminate markets because limitless free energy would not eliminate all scarcity.