Differences between synaptic connections
Neurons are all about specialized structures having specialized roles. You've given a good justification for dendrites---an efficient way to fit lots of connections in a small space. A pyramidal neuron in cortex, for instance, will have tens of thousands of synapses. If you only had axosomatic connections, the soma would have to be enormous to fit all of them (and this would cause lots of other issues).

Dendritic structure also allows the cell more efficient electrical properties (see cable theory) and to process inputs independently. In fact, different parts of the dendrite are now thought of as independent computational compartments. For instance, the cell might want to selectively strengthen a single synapse or all the synapses on one dendritic branch. By physically isolating those synapses in small dendritic structures, it is easier to make those targeted changes without unwanted "crosstalk" on other synapses or cell activities. What's more, incoming connections from different areas often segregate into regions of the dendrite (e.g. in CA1 hippocampal pyramidal neurons, cortical connections to the most distant part of the dendrite, internal hippocampal connections to the part of the dendrite closer to the soma).

When a cell has a large dendrite (some neurons have no dendrites), its useful to think of axodendritic synapses as the normal inputs that contribute to fine-grained computation, and axosomatic and axoaxonic synapses as more global gates. These latter types take advantage of their location to short circuit the "normal" computation in the dendrites. An inhibitory axosomatic synapse, for example, will reduce the effect of all dendritic inputs when activated.