Fundamental reason is usage and the design that evolved based on it- mobile phone as the name suggests are meant to be used whenever and wherever, with periodic charging, unlike laptops, which are designed to work with / without being plugged in to power.
It seems technically possible, to work without a battery, if you build an electric circuit that simulates a battery in all respects (including the battery health pin which is usually the third pin on battery) as you can see here. Whether, such a circuit will work across OS versions and devices is not certain - Android considers battery to be an integral part of the system rather than an accessory and OS evolves in safety, longevity of battery, user friendly features, that support this - witness Battery Saver , automatic shut down at low battery percentage as examples. If the electronics (SMBus) detects that it is not an actual battery source, this circuit may fail
Views expressed in comments are valid pointers, in addition to mine