Lets get away from this nonsense that since test gear, TV's and most all electronics works well out of the box that every aspect of stereo gear should be the same. I don't know of ANY commercial or consumer product that routinely installs caps that are rated so much higher than the actual applied voltage. Were dealing with a rather unique set of circumstances here.
In this and related threads, the possibility that "burn in" effects might be due to unused electrolytic capacitor re-forming has not been questioned.
However, commercial and consumer products regularly use capacitors in circuits where they never come near their design ratings (significant de-rating to reduce risk of failure is common) or anything near maximum voltage might only be achieved under unusual circumstances -- maximum volume, maximum output level, maximum frequency, highest-numbered settings -- or never, if a high-voltage rated (but common) component is simply the cheapest for the given application.
The difference between restoring typical consumer gear or test equipment, vs stereo amplifiers and recapping speakers, is that consumer gear -- like old televisions and VCRs -- and test equipment will usually have caps replaced with modern brand-name new stock, ordered from high-volume suppliers (Mouser, RS, Farnell, etc.) and therefore likely of recent manufacture. They won't need to be re-formed. New-old-stock electrolytics will be
assumed to need re-forming, and so will be re-formed on the bench and/or the repaired unit will be brought up slowly via a dim-bulb tester or variac, so re-forming takes place before the unit is returned to service or to the customer.
Only vintage stereo amplifiers and stereo speakers are regularly recapped by owners or enthusiasts who may be purchasing and installing caps from boutique suppliers offering components of unknown age and provenance, and immediately return them to full service with the solder barely cooled -- or are having equipment "restored" by commercial recappers who may use decades-old shelf stock and release the gear with minimal testing. This may produce a situation where stereo gear is put into full service with capacitors essentially un-formed. Combine it with the relatively low-voltage AC applied to speaker crossover caps -- at least at low volume -- and I agree with you that speaker crossover caps are likely being put into use whilst needing to be re-formed, and are being re-formed slowly in use.
"Loud obnoxious squeals" are probably something else, though. No condition of a crossover cap -- bad or good -- should generate a signal. That sounds like some unrelated phenomenon, like oscillation in the amplifier or a problem with the source.