We don't. And how do we know, that the current chain has the heaviest Proof of Work in existence? We don't know that too. But there are incentives to share blocks, which is why miners do that in the first place. And there are already some incentives, to show publicly the progress of cryptography, and be rewarded directly in BTC for doing just that. If you think, that there is not enough incentive, then again: put more coins in, or invent a better puzzle. What else can be done?
These examples are not related imo.
You are comparing a shadow chain to a tech advancement.
To create a longer secret chain than the existing one, miners need to re-direct their resources to the shadow chain. People will notice it because while the total worldwide electricity consumption is increasing, the hashrate on the known chain won’t increase proportionally. It is also a big gamble. Miners are not gamblers.
Tech on the other hand has always been doing what I have said. The inventors always let us use the beta and never give us the full product till they come up with a better product than what they currently have.
