Sealant used to prevent water getting between bath and wall?
The rubbery sealant is bathroom (or general-purpose) silicone caulk. As to why they don't use it between every tile, the answer is that it shouldn't be necessary; except for the one row of tile overhanging the "backsplash" of a "built-in" tub (helps keep minor splashes and overflow from seeping into the wall behind the tub), all tiles should be fixed to the wall, and unless the bathtub is not properly supported from underneath the weight of water should have only a minimal effect on stretching and shrinkage of that wall. If the wall IS stretching and shrinking enough to crack and flake the grout, it will probably also be affecting the tiles' adhesion to the wall, and you will, sooner than you should have to, be paying someone else to repair or replace the tile.

It's also a cost-benefits thing. Grout is very easy to apply; after applying the tiles to the backing, simply load a trowel with the grout mix, and scrape it over tile and gap alike, pressing the grout into the gaps. Then, with a damp rag, wipe off the tile, leaving grout in the gaps. Contrast that with going over every gap between tiles with a caulk gun, carefully applying just the right amount of caulk; caulking is precision work if you want it to look good. You can grout a full shower in less than an hour; you'd be there all day with a caulk gun.