Why does underwinding create topological strain of DNA?
The double helical structure of DNA with ~10.5 bp/turn is thermodynamically favorable. Any perturbation from this results in strain. Thus, if DNA is under wound, it is favourable for it to adopt a negative supercoil to return to ~10.5 bp/turn.

That said, negative supercoiling and DNA melting are in fact in some kind of equilibrium. This is important for processes such as transcription and replication which require ssDNA.