I am a beginner in motivic homotopy theory and motivic cohomology and have just begun reading books by Dundas et al. and Mazza-Voevodsky-Weibel. I have two basic questions:

Why is the question of $\mathbb A^1$-invariance of certain sheaves (for example, motivic homotopy groups $\pi_i^{\mathbb A^1}$, cohomology of a homotopy invariant presheaf with transfers etc) so important in motivic cohomology? Is it because the projection maps $X \times \mathbb A^1 \to X$ are all

*inverted*in the motivic homotopy category?What difference does it make to motivic homotopy theory if on one hand one takes spaces with base-point and on the other one takes spaces themselves (no base-points)? I can see that Spaces with basepoint are required in order to be able to define the higher $\mathbb A^1$-homotopy groups $\pi_i^{\mathbb A^1}$ of a simplicial sheaf, for $i \geq 1$.