Some people are worried about the wellbeing of mining in the late 21th century if the fee market isn't enough to maintain the hashrate constant. But a tail emission which results in a removal of the 21 million BTC limit, like Monero implemented it, seems to be rejected categorically by Bitcoiners. And I can totally understand why: the 21 million limit is a symbol for Bitcoin's "hard money" character, so it's likely that a removal would result in a mass exodus of investors and perhaps even in a hard fork.

I have recently thought a bit about possible ideas to implement a tail emission, i.e. a continuous block reward, without touching the 21 million limit.

I remembered two ideas which were briefly mentioned I think in other discussions, but I haven't seen them really discussed:

1) Burn a part of the transaction fees and distribute them later (e.g. in the next halving period) in the form of a tail emission. This means that the supply will not be touched at all.

An example: The Bitcoin protocol is modified to require a proof-of-burn of 500 satoshis per kB of each transaction. A regular payment of ~128 bytes would result in about 65 sats as additional fee. In 210,000 blocks of the halving period, we achieve an average of 2 MB blocks, which result in 2100 BTC which can be distributed. This would allow us a block reward of 0.01 BTC for the next halving period without touching the supply.

What is true is that in this proposal we are basically transferring a part of the transaction fees into the future. But there is a crucial advantage for miners: at least a part of the reward would be predictable. And in with "additional" block rewards all we do is diluting the supply anyway.

2) Create a second official Bitcoin token which is distributed in an infinite manner, e.g. 1 per block, to miners, from a specific block on.

The crucial question here seems to be: where should the demand for this token come from, isn't it just an altcoin and would thus be a flawed alternative to simply merge-mine with some altchain?

First, in contrast to a simple altcoin, you would benefit from Bitcoin's blockchain security. An idea could be to restrict this token to simple transactions (and swaps from/to BTC) without any Bitcoin Script programmability, and assign their components a lower weight in the blocks. This would mean that if you transact often, you would like to do it with this token and not with the original BTC. Perhaps even some ideas from modern cryptography (zk proofs?) could be used to decrease the size of transactions further, e.g. creating a kind of "rollup on the BTC chain".

I have already seen similar proposals been mentioned, so they aren't my invention, but they weren't really discussed anywhere (at least I didn't find the discussions, any link would be very useful!). So what I would like to know: Are there there any unsurmountable problems with these proposals?