So by your method the bank would own 60%, the borrower 40% with a mortgage of 250k and a further rental liability of some description? This wouldn't do enough for people. Mortgage might drop by about €740 but then rental liability would eat most of that up. Debt forgiveness will have to involve some real benefit.
You are right, if we merely replace interest with rent it might not have a big enough impact on improving people's day to day finances. This is why it should be rolled up.
An example of this is as follows:
Mortgage €400k, Market Value €250k.
Bring the mortgage down to a manageble amount - say €300k (I'm assuming there are a lot of people who would be out of immediate trouble from a 25% reduction in mortgage payments).
For this €100k reduction, the bank takes 40% (100/250) ownership of the property.
Say a rental yield of 4% is set. The owner must pay the bank 40% of this or 1.6% of the market value of the property.
If the person is unable to pay this, it is knocked off their equity i.e. if they simply continue to make the payments on the €300k with no rent, after ten years their ownership drops a further 16% (1.6% * 10) to 44% of the property.
The advantage of this is that they are no forced to move out of their house and take a forced loss at a firesale price.
If their circumstances improve over the next 10 years they can start to buy back a full share of their house. Additionally if the house can be sold on better terms at a later date, the losses are not as severe as in the forced sale situation.
It does us no good to engage in mass forced sales in the current environment and equally it does us no good to pardon debts of people who may bounce back in the future.