It likely wont be as bad as it seems, because the lenders still want to get your credit card business, they know that means you will be cancelling an existing card. Alll they have to do is comply with the legislation. If the assessor must include existing card limits + new card limit, hardly anyone would get a new credit card. Its no different to refinancing a PL or HL, the decision is made on the 'post loan' expenses.
The smart banks will provide a way for the applicant to declare the current credit card limits, and which ones they are 'refinancing', and those wont be included in the credit assessment. After that its still unlikely that the credit card provider will demand proof the previous limit is cancelled, that would be too costly an administrative overhead. Rather the onus will be on the cardholder to make good on the cancellation. If they dont and then run into debt problems, the cardholder wont be able to claim the credit card company was irresponsible in approving the limit.