While classed as "Colpitts", the versions below are more easily biased, yet still uses similar-value resonant components. The circuit at left is similar to OP's non-oscillator, while the circuit at right has more reasonable component values in a lower-power circuit.
An oscillator is never used alone: it is designed to deliver AC power to a load...a consideration during design. A high-power oscillator might be used to deliver power by heating in an induction furnace. In such a device, you might see small inductor values having low reactance at the operating frequency, but not likely in the "Colpitts" format. High operating currents would be needed.
The Colpitts oscillator at left does oscillate if enough transistor bias current is applied - in this case about 20 mA. But oscillating amplitude is small. Collector voltage only swings about a volt. That's not much compared to the DC supply of 9V. Furthermore, the 9V DC supply must be well-fixed and stable. A series resistance of only 0.02 ohms kills oscillation. A 9V transistor-radio battery has perhaps 2 ohms of series resistance.
The circuit at right operates at much lower power, and consequently can deliver much less power to a load. It might be used to drive another electronic circuit. It is biased with less than 1 mA DC current, oscillating robustly. Collector voltage swings 18 volts peak-to-peak...if some power were extracted, amplitude would be smaller.
The circuit at right was designed by choosing inductive reactance of 50 ohms. If power extracted is small, a higher inductive reactance can be chosen, reducing the needed DC power required. The inductor is often the most lossy component: if its quality is high (high-Q), even less DC power is required.
Note that LTSPice allows inductors and capacitors to include (hidden) resistors that are not shown on the schematic (to reduce clutter). The inductors here both have series resistors: L1 has 0.03 ohm, L2 has 1.5 ohm.
The oscillator at left needs a kick to get it started, but only because SPICE has far less noise than real-life. It is started by providing an initial-condition, by specifying
.IC I(L1)=0. Thus, the inductor current rises from zero amps at t=0 seconds, up to the operating point of 20mA - this is a "kick".