The whole purpose of the Tesla coil configuration is to generate a very high voltage.
- The primary is grounded.
- The high voltage end of the secondary has a high voltage on it.
- You want them to be far apart, for insulation.
There are transformers where the primary is wound over the entire secondary. These have far better coupling coefficient, so can operate without needing resonance to overcome the very low coupling coefficient of the Tesla configuration. However, because the primary is now near to the secondary, this severely limits the maximum voltage that the secondary can achieve. We don't call such transformers Tesla coils.
Resonance allows the energy transfer from primary to secondary to take place over a period of many cycles, to cope with the very low coupling coefficient.
A good analogy is a child's swing, as an example of a pumped mechanical resonator. The child drives it, by shifting the position of their centre of mass. However they can only achieve a tiny deflection in the swing position with a single shift in their position. Their coefficient of coupling to the swing is very low. If they drive the swing over many cycles, by timing their body shifts correctly, they can then build up an appreciable amplitude on the swing.