Why can't a galvanic cell be a single cell?
Perhaps this isn't the full answer, but it probably plays a role. It is critical for galvanic cells that there not be any electronic conductivity through the cell between the two electrodes. If there is a path for electrons, they will take it which means the cell will spontaneously discharge and not do any useful work through the external circuit. Pure water is a very poor conductor but becomes conductive once ions are dissolved.

By comparison, the construction of a lithium ion cell is close to what you describe for a single chamber galvanic cell. There is a separator involved but mostly to keep the two electrodes from coming into direct contact. One reason this is possible is that the electrolyte is an organic solvent (usually ethylene carbonate, dimethyl carbonate, etc) and doesn't conduct electrons, even when the appropriate salt (eg. $\ce{LiPF6}$) is dissolved in it. There is no salt bridge in this cell, though it is clearly galvanic.

Regarding the electrolytic cell, I don't see any particular reason that you couldn't build one with a salt bridge, provided the salt-bridge let you balance the charges generated on each side. Maybe they're all presented as one beaker just because it's easier to make and there's not really any advantage to a salt bridge in this case.