According to my loudspeakers owner's manual (2-way cone type) recommendation: They should be "run-in" for a minimum of 200 hours prior to any critical listening. I found that they required at least 300 hours before the magic began. Fortunately, my preamplifier has a white noise generator input, which helped out. Not only did the loudspeakers benefit but my interconnects and loudspeaker cables as well. Really, it did.
This applies to loudspeakers that have magnets, surrounds, crossovers, etc. True full-range ESLs would be excluded as they have none of these components.
I prefer the term "run-in" to "burn-in" as I try not to let the "smoke out." LOL