You seem to have a low opinion of simulators.
My dislike of simulators stems from:
I am a grumpy old man.
If you want to learn electronics, then do the electronics, feel the components getting hot, burn your fingers with the soldering iron, smell the solder fumes, release the magic smoke (see my sig-line).
There are somethings which simulators do not do very well, like stray capacitance and inductance. As I am an RF enthusiast, the strays are what make a circuit work or fail quite often.
Did I mention something about my being grumpy?
Why do you think it won't show the frequency modulation?
All the text books show am FM modulated waveform in a highly exagerated manner with obvious changes in frequency, may be as much as 2:1 .
The reality of an FM modulated signal at 100Mhz viewed on an oscilloscope (real or simulated) is that the frequency change is a very small percentage of the carrier frequency.
That small change can be seen on a well triggered scope as the slight broadening of the sinewave trace after several cycles.
If the simulator had a spectrum analyser feature, then a wide deviation FM signal would be easily recognised.
Also, in this case, I am not sure that the simulator will actually simulate the FM effects due to the changes in parasitic capacitances within the transistor.
I have seen it postulated (I think it may have been by MrAl here on ETO) that the FM is actually due to loading of the tuned circuit by the collector resistance of the transistor. I did start to rig up an experiment to try and prove or disprove it, but real work got in the way and I dropped the idea.
So, that is why I was rather dismissive of the simulator, for better or worse.
JimB