Assumption 1: The 1 MB txn limit is binding for some reason.
Security should be measured by the ratio of the reward per block to the money supply. Currently, "security" is about 50/7,000,000= 7.1 * 10^-6
If there are 21 million instead of 7 million BTC in the money supply, the block reward will need to triple to 150 in order to maintain security, i.e. 150/21,000,000 = 7.1 * 10^-6
1 MB maximum is equivalent to about 4000 transactions per block. In order for 4000 transactions to yield 150 BTC, you would need a per txn fee of 150/4000=0.0375. Currently, 0.0375 BTC is worth about USD$0.50. This seems alright, but it could not last. With growth in the demand for txns, BTC will appreciate, leading to a much larger txn fee. For example, right now I doubt that there are even 500 txn per block.
If the # of txns per block increases by eight fold or more to reach 4000, we should expect at least an eight-fold appreciation of BTC vs. USD. This would increase the txn fee to USD$4.00.
Such a high txn fee would greatly undermine the usefulness of the technology.
Assumption 2: Assume the txn limit can be increased so as to maximize txn fee revenue. VISA processes about 1 million txn per 10 minutes (i.e. per block). Suppose Bitcoin makes each block 250 MB and handles the same txn velocity as VISA. Then a 150 BTC per block reward can be maintained with a txn fee of 150 BTC per block / 1 million txn per block = 0.00015 BTC/txn. This doesn't sound sound like much until you think about how much BTC will be worth under this scenario. Particularly important is the ratio of BTC's market cap to its txn volume. The more money is hoarded, the more onerous the txn fees need to be to protect security. I consider two possible BTC valuation scenarios . They are designed to represent upper and lower bounds on BTC market cap.
Your assumptions are invalid. I'm not talking about your stated assumptions, but your unstated ones.
First invalid unstated assumption: The ratio of block reward to total BTC supply is meaningful. You actually do state this assumption, but you do it in a way that makes it look like an established fact, and not the baseless assumption that it is. Rather than give it a cute and emotionally charged name like
security, I prefer to name this ratio
cerulean. Do you have any reasons to believe that anyone should care about this ratio?
Second invalid unstated assumption: The current value of
cerulean, or
security as you may still prefer to call it, is the correct value, even though this value is an accident of time. If you had written this post a day earlier, or even 10 minutes, or for that matter 10 minutes later, the value of the ratio would be different. Not by much, if the interval is small, but by a lot if we get into months. What was special about yesterday that make that day's value correct? How did bitcoin even get this far, since a month ago, the ratio was different by 3%, and a whopping 38% a year ago?
Third invalid unstated assumption: Bitcoin needs to be the best store of value, or the best medium of transaction. This is a false dichotomy. There are other things it can do, and even if it were only used for those two things, it wouldn't need to be the best at either of them to be successful.
I would keep going, but in your second scenario, your thoughts get very non-linear, and I can no longer follow you. In particular, your sentence "This doesn't sound sound [sic] like much until you think about how much BTC will be worth under this scenario." could be replaced, with no loss of clarity, by "This doesn't sound like much until you think about a unicorn appearing right in front of you.". I think that we are supposed to assume that the
name of the unicorn value of bitcoins is so horrible, in some way, that you can't even speak of it.
Here are some things you should think about.
1) Bitcoin does not need to replace VISA. VISA does things that bitcoin cannot do, such as providing a way to roll back a transaction. In a bitcoin future, VISA will still exist, and still do the same things it does today, just with one more currency.
2) Even at $4.00, a bitcoin transaction is still far cheaper than several entire classes of financial transfers, like bank wire transfers. These types of transfers currently do happen today in the real world, even though they cost at least an order of magnitude more than $4.00.
3) Transaction fees do not cause security any more than ATM fees do. People with an interest in the security of the system will continue to work on the chain, to at least some extent, even if the reward is zero.
4) Proof-of-stake is still stupid. I'm sorry that there is no nice way to say that. I think that you start to go off the rails when you think of proof-of-work, which is also pretty stupid when looked at in positive terms. If you think that proof-of-work as something that the network should reward you for, then nothing else in the system makes any sense. What you need to do is think in terms of proving that someone else has to do an infeasible amount of work to roll back the clock. We don't care about anything else, really.