That's not a positive. I've found Eminence to be on average within 5% of spec out of the box, needing minimal break-in to work to full potential. I once had some PAudio drivers that ran 25% high and were for all intents and purposes unusable without breaking in. Some things are best when tight, surrounds aren't.
Not totally OT automobile engines do break in. The initial tight fit of the parts causes higher friction. With a bit of wear the engine works better. My last three cars have all had gas mileage readouts and all three improved after 6 months or so of driving.
By a salesperson trained to tell the customer what he wants to hear.

It's possible that there are companies that break in their drivers or cabs, but I'm not aware of any,
This is a great example of the fact that we all seem to be talking about two very different things.
1) Can things change over time (cars, speakers, etc.)?
I don't think anyone is saying that they don't, and as Jorg said, the Celestion's seem to behave differently out of the box, and hence take a bit of time to settle in versus the Eminence drivers used in the vast majority of bass cabs.
2) Do you have to perform some sort of fancy, formal break-in, like playing a special tone through a speaker at home, or playing programmed material through it for hours before use?
I believe most of us are saying no. In the case of the vast majority of speakers, play the darn things and be happy. After 4 or 5 (or 10) gigs, as you point out above, some speakers will sound exactly the same, others might extend a bit lower than right out of the box (assuming you got a new one and not one that had been pounded on in a retail store for a month before purchase).
So, to me, two different questions:
'Do you need to do some sort of formal speaker break-in?'.... the answer seems to be 'no' in the vast majority of cases.
'Will my speaker sound different after I play it for a while?'... the answer seems to be 'maybe', depending on the specific speaker brand and design used in various cabs.
Same thing with a modern car... will the gas mileage go up a bit over time... in most cased 'yes'. Do you need to do anything special to achieve this.... 'no'!