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.
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.
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.
I don't have time to completely argument, however, in brief:
1) No problem with credit cards or debit card: I already use them. I could just as easily use them with bitcoins. The issue is the fees that should be low.
2) Paypal is not a payment gateway, but a payment processor. It handles each transaction entirely. Both sender and receiver need to be registered on it. I propose instead a network of interoperable payment gateways where each user can choose its gateway (the cheaper or faster or trustworthy, even if the trust needed if almost zero). To have a transaction among two people, they do not need to use the same gateway.
3) If you want privacy, you can just choose a payment gateway in a country where there is no need to record transactions. A payment gateway could even be located into TOR.
The bandwidth and the storage space issues have already been discussed. You cannot get away with it by just saying that storage is cheap... We must abandon this kind of religious thinking where we just hope that storage will get cheaper and network speed bigger just as much as we need.
Off course there are going to be advancements but the pace of such advancements is not goint to allow to cope with the huge increase of the number of transactions.
In any case, as I said before, you can still use direct transactions (but fees are going to be higher).
Best regards,
ilpirata79