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Off-chain transactions for small or micro payments does not forbid you to send money to a friend of yours directly (through the blockchain - you may just have to pay a relatively high fee).
Yes and one of Bitcoins big advantages are the small fees. A cheap, fast payment system without the need of intermediaries, that is one huge part of bitcoin imho.Quote
The problem is that one thing if what we want, another thing is what we actually CAN have. World is made of constraints. You just cannot record everything, but in any case why would you do that? I don't care if my coffee transaction does not get into the block chain (as a single transaction). Intermediares that lower the required fees and speed up transaction times are just good.
We can have bitcoins without intermediaries. I care if I depended on an intermediary. I don't want companies between me and my money or the money transfer system. I can have that already, it's called a credit card 
. There is no problem with recording everything. Disk space is already very cheap and it gets cheaper and cheaper. If you have concerns about your privacy, I can guarantee you, that these intermediaries will be obligated to track everything, so you might have less privacy than with the existing system, which gives you enough room for anonymity if you really care. Intermediaries make the system unnecessary complicated. And they are absolutely not needed.Quote
Consider that such intermediares (that I call payment gateways) could even increase user privacy, by aggregating several small transactions into a big one where the information about the component transactions is lost.
PayPal can be called payment gateway as well. For example, if we installed some kind of "no small transactions" system, there is a big chance, that companies like Ebay become these intermediaries. And as I stated above, there will be no privacy as soon as there is some kind of controllable intermediary.I'm not saying I have the perfect solution, but there are some test-worthy ideas out there and there is no technical reason to limit transactions on the blockchain.