Almost every serious product needs some level of certification. And for almost every serious product, there will be multiple critical parts for which there is no drop-in second source with identical characteristics. And even when second sources exist, there will be no more guarantees that they will be produced longer than the original part. And for almost every serious product, the engineering costs for re-design and re-certification are high if parts do end up needing replaced.
You are not in some special situation here - this is life for electronics designers and producers the world over. There are all sorts of ways to limit the risks and limit the resulting costs. Requiring "second source" for one component is one possibility - but it is rarely a good idea overall. It's better to run the risk of having to pay some extra costs for a re-certification ten years in the future than to be guaranteed to pay extra costs now for trying to design the product with a hopelessly outdated device.
But one thing you can be sure of - there are no fixed answers that always apply. You deal with each project in the way that works best for that project.
And if you are a good designer and project partner, when a customer makes a requirement that you think is likely to be a bad idea, you question it. You challenge it. You try to find alternative solutions that will give a better result overall for the project. (It's unlikely, however, that the best alternative is "fire the manager" !) The customer is /not/ always right - at least not at first. As an electronics designer and consultant, it is part of your job to tell the customer if you don't think they are asking for the right thing - if you give them what they ask for, not what they want or need, then you are doing them a disservice. Of course this will mean that sometimes a customer will move on and find an alternative supplier. That's part of the job too.
Sure - and what percentage of electronics development projects do these account for? Rounded to the nearest percent, nothing. (And I've worked on a few safety-related projects - second source was never an issue.)