There must be amplifiers in the world that work well with almost any speaker and are consistent competent performers that are also reasonably affordable.There aren't.
Generally speaking, transistor amps have a hard time sounding right on ESLs because the impedance curve of an ESL isn't a map of its efficiency unlike many box speakers. Part of this has to do with the simple fact that an ESL isn't in a box :) As a result most solid state amps sound too bright on ESLs (and they already have a reputation of sounding too bright as it is).
If brightness and harshness is a problem for you, then you are more likely to gravitate towards tube amps. Tubes tend to make less of the higher ordered harmonics that the ear uses to sense sound pressure (and this is keenly sensitive to such harmonics, throw in the Fletcher-Munson curve and you have a problem). This is why tubes and tube amplifiers are still in production 60 years after being declared 'obsolete'. It just happens that tubes obey the rules of human hearing better than transistors.
You don't have to know anything technical here- all you have to know is that tubes are still around because people want them. Before you can have a 'benchmark' amplifier, you have to solve the distortion issues that separate tubes and transistors. My advice is don't hold your breath.