To answer your question why diodes are advisable:
coils don't like it when their current changes, and when switched off they'll try to keep the current flowing (energy coming from their magnetic field. Compare with the coil's dual, the capacitor, which will resist changes in voltage. There it's the electric field which has to be in-/decreased). Current flowing from V+ to the transistor's collector. You would think that this causes the same voltage drop as when switched on and that the collector voltage will be low.
The important thing is that the coil now doesn't work as a load but as a source, and in a source current flows from - to +. This means that the collector voltage will be higher than V+. And this is what the collector must be protected against. How? By shorting the higher voltage to V+ via the diode.
The 2803A has the diodes integrated.