Paying and holding rent during disputes

I am currently in an arduous process to have urgent maintenance done - however, it has been three weeks with no progress so far. Of course, I have been looking at various types of recourse (though I am unfamiliar with how arduous those are). One that struck me as quite interesting is the "Consumer Affair's Victoria Rent Special Account", where the rent can be paid and held until the repairs are complete - presumably satisfying that the tenant must pay rent but preventing the landlord from accessing it while they fail at their obligations. I have no idea the process of taking this action is (any information is welcome), but it did make me think: what if this were the norm?

What if tenants got to choose their own property manager (separate from the property manager that the landlord chooses), and they have a holding account that routinely keeps the rent if there are outstanding repairs? At the moment the landlord chooses the rental agency - and can change it whenever they feel like with no discussion with the tenants - which means that the tenants have obviously no true representation (even if they choose a rental because of the agency, they cannot guarantee that the agency will be used for the entire rental period).

This would give renters an ability to choose who represents them to protect their rights, as well as having a person who is paid to protect their rights (as landlords and agencies are paid to protect the landlord's rights, but the renter must pursue their rights in their spare time). It would also give the representative leverage to compel the landlord and landlord's agent to complete repairs, and so on.

Where would the money come from? Most economists propose that rents are generally set as high as they can be by the market, so that any tax on rents would "come out of the landlord's end" (that is, if the landlord raised the price renters would not be able to pay it and the landlord would have to lower it again to get an income). This means that if a percentage of rent went to the tenant's agency, it would come out of the landlord's end, without unduly affecting the rental price.

Anyway, any thoughts on the idea, or alternative proposals, are appreciated, and it will give me something to look through while I continually follow up with my current issues.