More blocksize essentially means more opportunity to capture transaction fees. This necessarily leads to an incentive to create bigger and bigger blocks therefore considerably increasing the cost of running a full node.
Yes but...
1. non mining nodes are already doing this altruistically.
Not necessarily. Payment processors have an interest to run a full node to more efficiently broadcast their transactions to the network.
You'd be surprised by the amount of wallet services provider that don't actually run a full node.
Do you have anything that can supports that claim or is it just an assumption?
It is well known that blockchain.info for example did not run their own node until very recently. There was a lot of discussion about this on the dev mailing list. A lot of companies rely on services like chain.com, blockcypher.com, etc. They have somewhat valid reasons as they don't have to build the whole software infrastructure for node indexing that these services have already built.