You are really talking about technical debt. Maybe a metaphor would help your managers. I often compare the effect of technical debt in software to cooking in a dirty kitchen. If the sink and counters and stove are piled with dirty dishes and there is trash on the floor, it takes longer to make a meal. However, the fastest way to prepare the very next meal is to work around the mess. Cleaning the kitchen, and keeping it clean, will delay the next meal, but will improve the delivery of all subsequent meals. And just as the hungry person in the dining room can’t see the messy kitchen, and won’t understand why you want to clean up before starting to cook, your management can’t see the mess in the code. You need to either show them the mess, or show the quality problems and delays that are caused by the mess.