I think it’s ok to realise that some conditions are too complex, costly or cumbersome to move into types, and use assertions instead. If anything, it makes for very clear documentation for people who have to maintain the code.
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I approve of this general principle. A cast (e.g. Int#asInstanceOf[PosInt]) is you—the programmer—claiming you know better than the compiler. If you can minimize the number of times you do this without compromising the certainty of your reasoning, then it's (ahem) a net positive.
A related idea is when you're safely handling failure cases, it makes sense to channel these into few places, rather than distributing the error-handling throughout your code. A larger part of your codebase will be total, and it will be easier to read.