What you are proposing is called "demurrage". It is an alternative form of inflation. Rather than devaluing money by printing more, you devalue it by canceling it or taxing it.
Anyway, it's not clear what the problem is that you want to solve.
thank you odolvlobo, we ha the same chat before about "demurrage" here in bitcointalk and I still could remember your key notes about the topic.
the oxidation fee may get stem from the idea that - by inventing btc - wants to introduce the digital form of gold as we find / lose in nature. everyday people find / buy / lose / reward gold all around but once you lose your address keys in btc, they never revive and get back to the circulation.
but with this oxidation fee in the protocol, the whole halving process could remain unchange but the reserve amount of remaining BTCs may increase in future, so rewards also increases. eventually I expect this oxidation fee with formal transaction fee could provide a continuous balanced profit for miners to keep high level of hashpower for the network and secure at all.