I agree with others in dismissing the possibility of Bitcoin dropping to $1,000, but ultimately, this is a thought experiment, and the possibility exists, even if it's only 1 in 1,000.
In any case, in my opinion, even if this highly improbable scenario were to occur, a recovery would happen quickly. As you mentioned in the likely reasons, many would see this as a golden opportunity to capitalize on the opportunity to buy Bitcoin at a very low price in the early years. Therefore, a recovery, even to just $10,000, would mean substantial profits, if it didn't rise even higher.
Of course, Bitcoin dropping to $1,000 would allow many individuals, not just companies and institutions, to buy large quantities, and this would allow the price to recover relatively quickly.
If everyone, from individuals to large organizations, took advantage of the opportunity to buy Bitcoin in large quantities when the price dropped. Do you think it has a chance of dropping to $1k? Clearly, if there is always strong demand waiting at lower prices, bitcoin will never fall to $1k. This also means that if Bitcoin still falls to $1k despite strong buying pressure beforehand, its chances of recovery are almost nonexistent. It will not surge as dramatically and rapidly as you might think.
If Bitcoin drops to $1k, meaning roughly a 99% decline from its peak, and that is no longer an opportunity but a disaster. Because no asset considered promising gets dumped that brutally, regardless of the reason.
You might be right, but this is a hypothetical scenario, and many unexpected things can happen.
Basically, as you mentioned, it's unlikely to drop to that price because there will always be strong demand at every dip, making it difficult for Bitcoin to fall to $1,000.
Let's suppose that, for some reason, there wasn't strong demand at the dip, or that selling pressure was stronger than buying pressure, and the price continued to fall to $1,000 and stabilized there. At that point, many people or companies would consider buying because it would be a great opportunity that wouldn't be repeated, and strong buying pressure would begin to push the price up.
Another possibility, which I consider unlikely, is that since Bitcoin has fallen so drastically, it will lose confidence, and no one will buy. In that case, yes, there won't be a rise; in fact, there might be further declines.