You're really serving to point out how useless natural weapons are here.
Even in an idealized scenario, their use is far fetched and applicable solely to martial-melee-oriented PCs who have been disarmed but must fight. How often does that happen? Once a campaign? Less? How many PCs will it even impact? It won't impact any caster who has any offensive cantrips, for example.
Assuming that natural weapons help in this kind of situation is pretty silly, especially as you're asserting non-moron captors.
With captors, no sane captor is going to ignore actually-dangerous claws or horns, are they? They're going to use countermeasures, indeed having natural weapons could leave you in a worse situation than other PCs because you're likely to be either separated, maimed intentionally (though I'd feel a DM was a little unkind to do that in most D&D campaigns, which have a sort of subtext of "fair play"), or have devices fitted to you to disable your natural weapons or just to prevent you from acting at all, which will consequentially disable you more than other PCs.
In a "no weapons" scenario, if your natural weapons are a real threat, you may simply be denied entry to such a place, kept at a distance other PCs are not, forced to wear devices preventing use of the weapons, or a variety of other situations. The odds of a guard who is terrified of you having even a dagger being fine with you having claws you could slit throats with or fangs to rip them out are non-existent. If weapons aren't totally banned - i.e. stuff like knives are allowed, you're probably going to be fine, but any total weapon exclusion zone? Nah.
What I'm saying is that this is beyond a corner-case situation.
The reality is that in 5E D&D, natural weapons that don't have additional abilities/effects associated with them have negligible value to and impact on a campaign.
Where they do have additional abilities, like a 1/rest free attack or move-and-attack they do have some real value, but they are still typically wildly, insanely, overvalued by WotC's D&D team to the point where there has to be some kind of weird rule in place about them, which does not stem from playtesting or game experience, merely being the bugbear of Crawford or whatever.