R3 or R4 is redundant, as they are both in series with the power supply?
At first sight, you'd be right, but let's see why are these resistors placed in there...
A resistor placed at the emitter of a BJT sets an amout of negative feedback. The current through the R shifts the emitter voltage so the base will be less polarized. In certain situations we would like to control how much total feedback we get by setting a little amount of negative feedback.
In Spain we have the aphorism "Las gallinas que entran por las que salen", that means "the chickens that enter, replace the ones that exit". Electrons flow from GND to Vcc, they don't have any other route to follow. However, the LC tank is a temporary Energy storage. That means that the electrons may not flow always at the same rate. Voltage at the collectors can be driven crazy. If that happens (when the oscillator amplitude surpasses the supply margins), both transistors can run out of active zone at the same time, and then the LC tank will no longer see everytime a high impedance. The wave gets distorted because part of the energy in the tank gets leaked.
Resistors at both emitters ensure that both transistors will be kept in active zone most of the time. In fact, a small amount of variation of one of the emitter resistors will ensure which transistor will mildly saturate. You don't usually want a hard saturation.
The funny thing is that if you remove one of the resistors and double the other's value, then you ensure that the transistor without the degeneration resistor will saturate hard, and both outputs get hardly distorted. But, because the other transistor is still in active mode, the differential voltage still holds and the output would still be a nice sine wave. Also, keeping output voltages symmetric from Vcc/2, and within supply range, is something desirable if you want to feed them into an opamp, for example.
What happens if the R approaches zero ohms?
Then there's is no significant amount of negative feedback, the both transistors will hard saturate, the wave will reach Vpp->2*Vcc, and you have an awful output.
Or a very high value?
If your LC tank had 0 ohm of total ESR (that is, an infinite Q factor), then the value of R at the emitters would not be so critical. You could set, R1=R2=100k, and R3=R4=10k. If you try these values in a simulator, the oscillator will still work:
https://www.falstad.com/s.php?s=RMFLVdBut with realistic values of ESR (my inductor should have ESR around 60-70 mOhms, and that capacitor about 10-20). With these values, R3+R4 above 220 will kill the gain. The emitter resistor values are a compromise between Vpp output, low distortion, stability under ambiental variations, and linearity.