These PDAs would be no more nor any less profitable for the banks than any other deposit account. I would presume that the banks wouldn't be offering interest-bearing deposit accounts if they were unprofitable. In fact, they are mad keen to get in deposits.
The banks would be perfectly free to offer whatever rate they would consider viable in the circumstances - subject to the condition I postulated to ensure competition and to protect against degrading the interest rate relative to other deposit products on offer by the bank. The banks would have to rebalance their products and rates with regard to these requirements. But at the end of the day the most competitive institutions would be able to offer the best rates.
The reason why compulsion would be necessary is not because they would be unprofitable but because the banks would be concerned that these products might displace much more lucrative (for the banks) pension products. Mind you, if the current pensions products are as wonderful as the pensions industry tells us in their advertising, and are worth all the fees and charges, the banks would have little to fear from being forced to provide these products.
Finally, the banks are forced to comply with all sorts of rules and provisos that they hate because they erode profitability. Tough on them. They are not private institutions with private rights any more. We own or effectively control most of them anyway and they will just have to get used to doing what they are told rather than being run on the assumption that, after the taxpayer has repaid all their debts, the banks will be handed back to their managements, and normal service - massive bonuses etc. will resume.
Perhaps a better idea would be to forget the banks altogether and allow credit unions that fulfilled certain capital and liquidity requirements to offer PDAs. They (and their members) would jump at the opportunity.