I think you're right, the parasitic capacitance will be too small and not stable enough. Parasitics don't always have the Q you would want, either.
Several separate topics:
Inductor Q---In practical inductors, a higher inductance does not mean better Q. With increasing number of turns, a smaller gauge wire is usually used, leading to a higher resistance. There's a balance to be struck
LC disadvantage----But I don't usually see an LC directly on a photodiode. That's probably because the resulting physical dimensions of such a circuit would be too susceptible to E/M fields.
Diode load---The output variable of a photodiode is current, not voltage. Converting to voltage too soon (such as right on the diode junction) invites interference and parasitic loads. Normally the first thing I see on a photodiode is a transconductance amplifier. That way the diode junction sees no voltage and capacitance essentially disappears from the frequency response equation.
Do you really want high Q---When you say "20 to 30 MHz" do you mean ONE frequency within that range, or to be sensitive to ANY frequency within the range? If the latter, high Q wouldn't be what you want anyways. A Q of 100 at 25MHz would leave you with a bandwidth of only 250 kHz.