By running it, the only advantage to you is that your blockchain stays updated. If you hadn't opened it in a couple weeks, then it might take a while to catch back up, delaying your payments, etc.

Also, by running it, you're benefiting the network as a whole, by adding another "node" which processes and relays transaction.

Miners in the end filter out transactions and process them in the final step of a transaction, but nodes that relay transactions are important too. This provides redundancy and filters out some of the obvious spam transactions so that there is less load on the miners (though at the moment, that's not a huge problem now- further along when bitcoin is more popular it could be a real concern).

Sorry, I shouldn't have used the word "processes."  Miners process transactions in the new block. Nodes simply relay new blocks to each other. Miners are doing the auditing and verification... nodes are distributing the results of that work. I think I got this right

The reward scheme is not optimal in Bitcoin. It relies on charity in order to produce some "public goods", thus they are underproduced.

This doesn't make Bitcoin unviable though. Bittorrent also works in practice even though seeding is pure charity.

Note that the reward scheme for mining isn't optimal either.  Once the block reward approaches zero, miners get rewarded for faster transaction processing, but they don't get rewarded for securing the network, which is their main purpose.  Securing the network is just a positive externality.   

The initial block reward is a direct reward for securing the network, however it is somewhat arbitrary and it ignores how much security consumers want and how much they are willing to pay for it.  It could be too high or it could be too low.

You can't give a direct reward for relaying because that would be too easy to abuse. Someone could just set up 1,000,000 clients on 1,000,000 IP addresses relaying among themselves, with a few outward connections, yet that wouldn't contribute much to the resilience  of the bitcoin network.

The topology and connectedness of running clients needs to be rewarded as well.

For now... What if/when we reach VISA volume of transactions.

I suppose you brought this up because of the microsoft paper. A more in depth discussion can be found here. Link to the microsoft paper within.
https://bt.irlbtc.com/view/51712.0

Care to explain that.  More transaction fees = more miners = stronger network.

There is no way for a user to pay to increase security under any transaction fee system.  There is only one level of security.  However setting min transaction fees could ensure that min level of security is provided based on transaction volume.

I run one because it is the only worthwhile contribution to the network that I can easily make at this time (other than trying to soak up some of the currency inflation.)

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BTW, I am making a bunch of very low power machines (several watts) which I hope to be viable full nodes, and could reasonably remain operational on solar/battery for a long time, and potentially on long distance wifi.

I bought some 6G microdrives to serve as the data storage for these hosts.  Just recently I looked at the node I run on my router and was alarmed to see the data size much bigger than I expected (at around 4G iirc...I'll do more analysis later, but my initial impression was that the block chain would be less size at this time.)  I do hope that the development team puts some focus on keeping things tight and efficient so that it is realistic to help support the network with minimal hardware.