A pretty decent video on power measurement. The trusty Bird is even shown.
The water cooled load is how we measured power at several transmitter sites.
It is very repeatable, unless the Laws of Physics somehow change!
I think why they aren't used so much these days isn't because of any great breakthroughs in other methods, but because they are expensive & need maintenance, which starts to cost extra when sites are no longer staffed, & contractors must be used.
"Good enough" is ever the enemy of "perfect", & other methods are "good enough".
The "digital" meter is impressive, but it relies upon accurate positioning of the probe on the coax or waveguide line, just as its analog counterparts do.
Once that probe is correctly fitted, any peculiarities can be corrected for.
Practically, unless there is a disastrous failure of the sampling section, the probe can sit there for decades, so "good enough" becomes "very good, indeed"!
On the subject of "the trusty Bird".
At 3:46 in, the big "Bird" meter has a pointer made of an offcut of red Dymo tape pointing to a particular point on the scale.
In practice, a Tech or EE would, in passing, check that the needle was at that mark showing the correct power level, as previously determined by a more sophisticated instrument.
In other instances,a list of scale corrections, usually with "normal" figures highlighted may be attached.
As I have previously pointed out, many Birds were used in situations where they offered a good "quick check" that all was well.
From the point of view of Broadcasting & Comms companies they were "dirt cheap".
I would say that is a "happy" bird meter.
Or, thinking at it from a continuous operation rather than looking at the duty cycle. It would be fun to play with one. I could do an unboxing video and blab about how good it is for a half hour as I personally don't have any way to test one.
The manufacture's specs for the Bird meters is clear. When the ham and CBers start calling them the gold standard and making claims about numbers without considering the errors, I laugh. There's no getting around that.