It's only taken me about 20 years on LF to actually think about, and calculate, this...

We all know we're supposed to attenuate harmonics and  unwanted signals, so most LF amplifiers, especially switching types,  incorporate a low pass filter - usually the traditional T or Pi design.

But I always felt the hi-Q antenna assembly would do a pretty good job of filtering in its own right, and didn't use any LPF on either the 700 Watt 137kHz Tx which has a tuned tank output (Ql = 6) or the 400W class E 475kHz unit.  

However, thought it was time to try to calculate the actual attenuation of harmonics.   So, using the inductance of the loading coil which goes up proportional to harmonic number, N,   Rrad of the antenna that goes up with N squared and a crude approximation of Rloss changing as 1/N, plugged all those into a spreadsheet and found the following on my 7m high Tee antenna

At 137kHz the relative radiated level of harmonics is between 50dB down at  2nd and 3rd, dropping to 45db at 8-9.    Considering the switcher PA plus tank is about -30dB to start with that looks well within the recommended -70dB for high power amps

At 475kHz low order are only 33dB down and higher up -30dB.  I don't have a figure for the class-E starting harmonic level, but IIRC it was of the same order as the 137 Tx, so again that looks near acceptable.

Of course, your antenna / loading coil assembly will differ, and larger antennas / smaller coils will not provide as much attenuation but it is still enough to suggest the 5th order filters in use on some designs are a bit OTT.

One thing I haven't considered is how distributed capacitance in the loading coil might compromise rejection of higher order harmonics, but that can be mitigated by the Tx producing less of them in the first place. 

Did the original Decca transmitters have any extra low -pass filtering ? 

Tee antenna design spreadsheet at http://www.g4jnt.com/DropF/teeantcalcs.xls