Burn in does have a measurable effect on speaker drivers. Basically you’re allowing the suspension and surrounds to become more pliable as they cycle over time, which affects the FS, Vas, and Q factors. A common outcome is that it can lower the overall tuning of the driver.
This is something that happens though after several hours of listening, so the traditional burn in of playing a continuous sine wave for 20+ hours isn’t really needed unless you want them burnt in faster.
For digital audio, imo it’s Speakers > room treatment > amp > preamp > cables > DAC/streamer/CD player
Or for analog sources it’s more like Speakers > phono cart/tape deck > room treatment > amp > preamp > cables