I ran 57s for a while, both a pair and a stacked pair with various amplifiers.
The amplifier matching is complex. To oversimplify, ESL57s present a complex load, with an impedance curve that changes damatically across frequencies. They are further difficult as the main load in the speaker is a transformer. The amplifier needs to be 'happy' with loads that run from near to 35 ohms around 100Hz to about 2 ohms at 15KHz.
Assuming a valve amplifier with an output transformer, this changing load is reflected by the transformer, so the actual valve (or valve pair) is similarly loaded by a wide impedance range. Push-pull designs are better suited in general, as despite the 'on paper' figures, 57s need reasonable power to work well. On the other hand, too much power is potentially damaging. Around 25-35 watts per channel is cited as ideal and I don't disagree.
For all the above reasons, against 'normal best practice' some (or even a lot of) negative feedback can be beneficial. Out of everything I tried, bought, borrowed with mine, the Radford STA15 was among the top, but needed a seriously good preamplifier to open up fully. I ran mine for a week with the Radford and a borrowed Kondo M7 and it was probably the best I ever had them sounding. The Leak Stereo 20 also performed very nicely indeed.
Surprisingly, the ones I didn't particularly like and that I thought never gelled well were Quads. The 405 and the 303 sounded flat and lifeless, and even Quad IIs never seemed to bring it all to life. Maybe some really well re-engineered variants would do the job, but it's a lot of money to experiment.
It would be interesting to revisit 57s with some of the newer valve amps around. The Icons and Prima Luna look sensible candidates, in particular those running EL34s in push-pull.