Firstly, yes it is. The fee that the sender is willing to pay depends on the amount he is transferring.
Secondly, the block size limit have a direct impact on transaction fees for obvious reasons.
The fee a sender is willing to pay may depend on the amount they are transferring, but that's irrelevant for the protocol. How low you can set your fee and still have your transaction be included within a reasonable time depends on how many inputs are being spent, not on how many coins. So if you received a lot of small transactions you'll pay a much higher fee for the same amount of coins than if you received just one large transaction.
Of course we could keep the block size limit to 1MB [...]
Block size limit has been effectively 2-4MB since SegWit's activation in 2017.
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The problem with dynamic block size limits is that in the end it's pretty much like having no block size at all.
Reducing blocksize limits in times of low demand will do nothing but artificially increase mining fees without saving any storage space -- the blocks would have been half empty anyways.
Increasing blocksize limits in times of high demand, based on the amount of fees paid relative to the amount being sent, would not only inflate the blocksize to whatever upper bound you'd define for the dynamic blocksize range -- which would in practice end up us the blocksize limit anyway -- you'd actually even penalize efficient transactions over inefficient ones (e.g. transactions consisting of a lot of small inputs like faucet rewards and thus take up a lot more blockspace). That is, you'd have a system that would incentivize detrimental behaviour which is rarely a good idea for something that is supposed to be self-regulating.
Also note that due to the use of change addresses it's not even possible to reliably determine the amount that is being sent. If I spend USD 10,- worth of Bitcoin with USD 90,-worth of Bitcoin going back to a change address, your proposed system would have to base the fee on the total of USD 100,- being moved.