If the protocol prevented them from grabbing that "burnt" part of the transaction fee, then they would not have this option. Or maybe you refer to the possibility that miners could reject that soft/hardfork? I think in this case everything would depend on the signalled support from economic nodes.
Then you'll have to mine your own blocks. Just as miners can't modify the block subsidy to give themselves double the reward, you also can't just rewrite the rules to take half the fees from them. You do realize that miners are the ones who actually write the blockchain. Try telling them, "Hey, we're going to pay you less now, please opt in to this new fork." Yeah... that's not going to happen, and without miners signalling support for this, the fork will be very short-lived.
The proposal would probably lead to a more stable hashrate even in periods with low onchain activity, so miners should support the proposal also for their own good to make it more predictable.
How is that for their own good? You're talking about rewarding miners in the future at the expense of miners working today. The logic of "suffer today so others can rest tomorrow" doesn't hold up from a miner's perspective. You're asking current operators to take a guaranteed cut now in exchange for a vague promise of “predictability” later, which isn't how capital-intensive, high-risk operations like mining work.
The reality is this:
BTC security depends entirely on its value. It's a self-securing protocol that has proven to work for many years, and I don't see why it wouldn't continue working long into the future. Over time, as block rewards decline, mining will be subsidized by Bitcoin holders one way or another.
When large corporations have a significant stake in
BTC, they'll want to support the network's security. Even the average user would likely be willing to contribute something to protect the value of their holdings if block rewards become too small to sustain the ecosystem. This kind of subsidy could be proportional to each person's holdings -- like paying a few dollars a year to keep your $10,000 safe. I don't think most people would object.
The technical mechanisms for how this would be implemented can be discussed when the time comes. But to me, it seems like the only viable long-term path forward -- if it ever becomes necessary. You might call it a tax, but it's really not. Just like you pay fees to move your coins, you may end up paying fees to store them securely.