The more of its stock a company holds, the less prone to devaluation it is. They have a higher control over how many shares can be sold at lower prices and will have less of a struggle buying back the volume that people are ditching at low prices. As a company you want to be constantly spending the money you bring in to pay less of it in taxes. That means you don't want to just stack cash on the side for a crash because even if the prices will be lower you can't guarantee the difference will be superior to what you'd pay in taxes and the issues you'd get with your employees and shareholders asking for a cut of the money in the meantime.

Planning to just buy back your own stock when it dips also means accepting your company's image will take a massive hit and you'll have a harder time getting future funding if it takes longer to go back up, or might lose some customer confidence and therefore sales.

Also, buying more of your own stock means that when the economic collapse does hit you don't have to fight board meetings with random people who just bought a massive share of your company for cheap before you could and are suddenly gunning for the heads of the company because they think they're the ones responsible for the loss of value, despite it being a much more complex overall economic context at fault. Even if that's not their intent, in a financial crisis you don't want your priorities to be blurry because of new-comers trying to make their mark on the company. You have to be able to say that you all previously agreed to a plan and that it should be applied without anyone suddenly questioning the validity of that plan.

Lastly, the shareholders who decide on the buybacks usually don't trade their stock, they collect dividends. A stock's price fluctuation does not always reflect a company's performance. Also, if they have a higher control over the decision-making of the company and were allocating a big chunk of ressources to buying back stock at higher prices, then they suddenly have an excess of available funds to split among themselves and not have their dividends reduced despite the macro-economic situation and the state of the company.

To be noted: I have no sources, this is the first time I wonder about this topic, 100% of this could be bs, but that would be my immediate analysis of the situation. If you have experience with buying back stock or something I said makes no sense, feel free to let me know, but keep in mind this is a 5 minute thought on the subject with no research.