Specnut,
Delta wings are indeed very good for high speed flight, and make the creation of very strong structures easy. But like most things in life they have their drawbacks.
They tend to have very low aspect ratios, so the induced drag is high, particularly at low speeds. They also require very high angles of attack at take-off and landing, which makes forward visibilty problematic. Look at what they had to do with the nose of Concorde to overcome this problem. Other problems include the difficulty in using trailing edge flaps without also using a tailplane or canard. It is of course possible to solve such problems, but they do exist.
For the mach numbers at which commercial aircraft currently cruise, high aspect ratio, supercritical swept wings provide a much better compromise.
FE Hoppy,
As you have said, supercritical wings also increase Mcrit. They may be considered to be a form of Area Rule, in that reducing the camber reduces the rate of change of cross-sectional area. This reduces airflow accelerations, which in turn increases Mcrit and reduces the intensity of the shock waves when they finally occur.
In most cases, some of the potential increase in Mcrit is traded off to enable thicker cross-sections to be used, thereby making the wings stiffer and increasing fuel storage space. In effect the supercritical section increases Mcrit, then the thicker section reduces it a bit, but still leaving it higher than for a conventional wing of equal thickness.