I propose that a fee recovery rate field be added to the bitcoin header. The purpose is to guarantee adequate competition and blockchain security. The fee recovery rate will default to 100 percent. If the number of nodes falls below an "ideal" level, the recovery rate is reduced along a defined curve.
Which header are you talking about? The block header?
How do you intend to determine the number of "nodes"?
Please define what you mean by "node". Are you talking about miners? Mining pools? Relay nodes? Nodes that store the entire blockchain?
How will you verify that the value placed in the block header by the miner (or mining pool) was accurate when they built the block header?
The value of the fee recovery rate at network size one (monopoly) is zero (e.g. no recovery). This prevents a transaction processor from becoming a monopoly in that as a transaction processor reduces its pricing below competitive rates, the fee recovery rate reduces their profit. The exact number for the "ideal" is yet to be determined. The method to determine if the number of nodes is below the ideal is yet to be determined. The curve for the reduction of the fee recovery ratio is yet to be determined. The field will probably not be required until 2140 but may then be essential to prevent a monopoly.
You've got an awful lot of stuff that is "yet to be determined". Please work out the details of your proposal and let us know when you find a way to make it work. Currently, your proposal is about as useful as declaring:
"I propose that we require everyone to behave in an honest and trustworthy manner. How we will determine if they are trustworthy is yet to be determined. How we will tell if they behave in a trust worthy manner is yet to be determined. How to enforce the trustworthy behavior is yet to be determined. This proposal will prevent all scamming in the future."