It seems like there are 3 sub-questions to this question:
Adding liquid in the pan creates steam, a moist, hot gas which is able to move between the solids of the fond and lift the fond from the bottom of the pan.
The majority of the relevant food molecules in the fond, created from the Maillard reaction and caramelization, are water soluble. (The Maillard Reaction produces hundreds of products, only 8 of which are relevant factors on flavor and aroma, 6 of which are water soluble.) Since the flavors inside the fond are potent, dissolving them into water makes them available to our taste buds.
Regarding burnt bits stuck to the side
I have to presume from the scenario you provided that, since you "heat [your] stainless steel pan", you have left the bits there from your previous cook and allowed them to dry. The lack of moisture content will make the bits more difficult for the steam to remove. When we deglaze the fond from the bottom of the pan, the fond already contains some level of moisture and is able to be easily removed by the steam. When you allow, presumably now overcooked and dried out, bits of food to sit on the pan and become moisture-less, hardened carbon, it will take more effort to remove.
For an analogy, think of clay. If you throw it in a pan and immediately wash it off, it will come off with relative ease, but if you let it sit (even without heat) and simply dry out, you would have to crack and and chip it away, or cover it in water and let it sit and absorb moisture for some time before you could wipe it away.