My own inclination is to say you'll end up with a bunch of people all having the same skills.
Good observation. And to embellish what Ryryguy said, a key design principle of 4e is the teamwork vs. solo dynamic, as well as the delineation of party roles. (Both combat and exploration roles. And it just so happens that strikers in D&D have always had the most & coolest skills.)
Therefore, as long as the players make sure they have every role and power source covered, it's a good bet they'll have every skill covered as well (without having to compare notes, which sometimes leads to bitter accusations of "Metagaming!") Meanwhile, a good DM is going to set up situations and skill challenges that will test the weak points of the party. If nobody bothered to take Streetwise, they will run into obstacles sooner or later, no matter if everyone took Insight.
I see class skill rules as sensible, as well as a carefully written mechanic in 3.0, 3.5, and 4.0. I have always run them by the book. 4.0 offers some built-in ways around these restrictions -- the main one being the Skill Training feat, whereby you can have any skill your heart desires by the time you reach paragon tier. Eladrin Education is a similar workaround. A perfect example of
Exception-based rules design. Is it really necessary to drop class skill restrictions for the rest of the starting characters?
I'd probably only grant a +3 Training bonus to outside-of-class abilities for standard Skill Training, and only an additional +2 for Skill Focus.
Those numbers do make sense, and I might use them.
And that reminds me... I also allow every PC to split one of their training slots, +2 to two class skills instead of +5 to one. The split training also stacks with full training (+7 total) should the PC choose the Skill Training feat later in her career.
Anyone else?