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Presumably developers are the one's estimating how long things take. (If they're not, you have even bigger problems and I'm sorry.) The time to make it safe should automatically be included in those estimates.
Moreover, making it safe shouldn't be a separate part of the process. It should just be part of how you write software. It's either safe or it doesn't exist at all. (Compare this to how organizations like Google deal with concurrency: it's built in from the start.)
A reputable engineer wouldn't design and build a bridge which might collapse. A developer shouldn't build software which puts lives at risk, regardless of management pressure.
If they refuse to relent, there are plenty of jobs where safety isn't critical.