Control pointed it out. Im not sure what state you're in, or if it matters, but being able to maintain habitability within the house is required like you stated, and access to fix these problems must be permitted by the tenant. You actually have to take them to court if they do not allow you access to fix the repair, as that is then causing damage to your property. As it "should" be one of the things listed on your lease that it is an offense that would warrant an eviction.
Also, within the lease - stop covering stupid shit like Dishwashers, washer and dryer, stove, refrigerator, etc. Make that the tenants responsibility to replace. You have the tenants inspect and use each appliance when they move in to show that they are in working condition and give them a predetermined amount of time to bring any issues with the appliances up to you if they are broken after the fact. I typically give a week on mine. When they move out, you inspect the appliances and if they are not in working condition - you can bill them, or take them to court for the damages. If you're footing the bill for the appliances, whats to keep them from doing stupid shit like washing their boots covered in mud in the dishwasher? Or holding the door to the refrigerator open to cool the house? Or the opposite for the stove? etc. etc.