Ruin Explorer
Legend
You're really serving to point out how useless natural weapons are here.There won't always be an improvised club sitting within arm's reach. I'll grant that in many circumstances there will be one nearby, but you may have to spend you first turn disengaging (or taking opportunity attacks) and running over to grab it.
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.The two most common scenarios where PCs don't have weapons (IME) are when they've either been captured or gone to a city that requires their weapons be left at the gate.
In the former, unless the captors are quite stupid or the PCs exceptionally clever, there may be no way to acquire an improvised weapon in advance.
In the latter, you could acquire an improvised weapon, but the guards would probably give you a hard time if you're walking around with a chair leg shoved through your belt. You could maybe hide it in your backpack, but then it's an action to remove and you've basically wasted your first turn anyway.
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.