Why does the 74AC04 not invert the 14.31818 MHz frequency

The largest single factor is usually inductor size. If you eg double frequency you can generally halve inductance (as the impedance of a pure inductor is proportional to frequency). In practice a number of factors apply so that it's not a directly linear relationship, but good enough.

If you need a peak current of say 1A then the time taken to ramp up from 0 to 1A is related mainly to inductance and applied voltage. If the inductor is say 10 x smaller the current ramps at ~ 10x the rate. The discharge time is also similarly speeded up and the overall cycle is faster so operating frequency is higher. You can look at this as the smaller inductor causing higher frequency operation or of the higher frequency allowing smaller inductors.

If the text mentioned thyristors in that context it is probably either an old one or is dealing with extremely high power levels. Nowadays, for most purposes inverters would usually use either MOSFETs or IGBTs. The very largest inverters may still use Thyratron valves - such as the many MegaWatt units used for DC to AC power conversion for DC submarine cables.

In typical portable modern applications an inverter which may have been operated at 100 kHz or less 10+ years ago is now liable to operate at 500 kHz to 2 MHz and a few operate at higher again. At 1 MHz+ and power levels of say a few Watts the inductor size may be 10%-20% of the size at 100 kHz and the inductor may still dominate the overall size.

Note that current carrying capacity ~ proportional to wire area but inductance is proportional to turns squared. This does not mean though that core size changes only with sqrt of frequency as you have issues of core cross section, core path length, winding window size and more to add to the fun.

Edit: Upon reflection I don't think this is the culprit in this case, I think Dave Tweed's comment is where the issue is, but I'll leave this in case someone runs into a spikier noise problem.

I suspect that a switching power supply is causing the problem. Here is the schematic (from Jan Panteltje) of a cheap eBay supply.

It's not perfect, Jan got the 1M connected to the MOSFET source, it actually goes to +300V.

Anyway, the point is this thing is kind of a self-oscillating flyback that runs at about 500kHz, with zero EMI considerations. It would certainly fail FCC testing, and hence is actually illegal to sell in the US. No common mode filter on the input, no shielding etc. It drove all his instrumentation up the wall.

Good supplies can still cause some interference, but if you have something like this it's like setting your 'scope up next to a radio transmitter.

If you have such a supply, see if the noise is still there with the Arduino turned off but the supply turned on, and if it goes away when the power is cut you've found the source.