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To be able to process the same number of transaction of VISA, Bitcoin should grow x2,000.
The size of blocks should go up ~1.000x at least to accommodate so many transactions.
And we will not just want to take VISA burden, we want, also, offer a service to the currently unbanked (being humans or DACs).
In the block size increase 50% every year, it will take 20 years to take over VISA alone; never mind the unbanked and DAcs.
You're not thinking about safety. Yes it would be nice for bitcoin to be able to handle 2000 as many transactions as it can now, however that is not as important as keeping bitcoin decentralized. Let's keep in mind why bitcoin was created: to create a digital gold standard so that people could protect their assets from central banks. If bitcoin also becomes a ubiquitous payment system that would be great, but not if it comes at the expense of decentralization.
Mining will need to be self sufficient using just fees and without block rewards in the long run.
So, if we take the capability of VISA network as a goal, we need at least 0.01 $ fee per transaction to give the miners the same amount of money they get today. And the minimum block size to be able to do so is very large to accommodate at least 4.000 transactions/second (and VISA process 8.000 transactions per second during high traffic days).
Decentralization is the main goal, because it make the network censor resistant.
But what make possible to maintain decentralization is openness. Anyone, no matter who, can connect and join the network if he has the resources to do so.
Miners need to distribute their block faster first to other miners and then to other nodes. If they distribute their block to other miners first, these miners will start to mine the next block earlier. If a miner was able to flash his blocks to the core nodes of network instantly (E.G. broadcast by DVB-T), but not to the (hash rate) majority of the miners, his ability to communicate would not count a lot, because the core nodes would be exposed to a longer competing chain shortly after. The core nodes just need to download the new blocks from the miners and/or offer them to other core nodes to be able to check the blocks, they don't mine, so they don't need the new blocks in a matter of seconds after they are discovered.
As with many different P2P networks, they work better if different nodes organize themselves in different ways/strata.
Just now, miners (usually miners pools) make large investments in mining rigs and related HW, SW, labor, power and real estate. They can afford to buy enough bandwidth to disperse blocks between themselves in a matter of seconds. More so if there is a Reverse lookup table and they just need to exchange mainly references to the Tx included and not the actual data.
The rationale to grow faster now with the block size exist because when the block reward will be halved, the revenues of the miners will halve if the price do not at least double.
The single fees can not grow x100 to compensate the reduction of the reward in just few months. They must be able to grow in number to compensate the diminishing reward, not become more costly for the consumer.
At least there must be room to allow this grow to happen.
Now a transaction cost 18$ (miners income = reward + fees). It is obviously impossible to sustain this costs if it came out directly from the users.
https://blockchain.info/it/charts/cost-per-transactionThe network must be able to manage the 1000 times the current transactions to bring the cost down to 1.8 cents from 18 $. Currently we have around 300 KB blocks, so the block size should increase to 300 MB (at least). Make it 600 MB to bring it down to 1 cent and 1 GB to compete with VISA.
The network will grow proportionally faster now than in the future, when it will have taken larger part of the market of payments. The curve will be something resembling an asymptotic curve to some level (E.G. 10x VISA) or linear increase (VISA + x transactions/year). But the steepest part will happen now and in the near future (4-6 years and no more).