But aside from that and speaking more broadly, very few financial service providers accept bearer shares companies. Those that do usually require that the bearer shares are kept by a custodian, and will ask for evidence thereof on a recurring basis.
If access to fiat banking/payments for the entity itself isn't a concern, then consider how the bearer shares company can taint a larger group structure. If that company owns other companies, those companies will be judged based on the bearer shares company.
Then there's the practical downside of simply losing track of where the shares are, at which point the company's ownership cannot be determined anymore. Or if someone steals the shares, they are the effective owner of the company until arrested and/or prosecuted for the theft.