The answer is, you simply upgrade the bike and pedestrian infrastructure at the same time as you do any other road work, and make it against the rules to do otherwise. So the roads that need repaving most urgently still get it, but they just get bike lanes and sidewalks urgently, too.

As for your previous pearl-clutching, which I have now found the patience to respond to:

1. Emergency vehicles have to be able to deal with shitty roads (including unpaved roads) already, so your first bullet point isn't a thing.
2. Traffic would not "increase exponentially" by having fewer usable roads. In fact, it's the opposite: that's what happens when you expand roads. What actually would happen is that people would be driven to alternatives, such as reducing trips, biking, walking, etc.
3. This is almost too nonsensical to address. Making roads worse is essentially traffic calming, and would increase safety.
4. This is too nonsensical to address. Pure hysterical bullshit.