If it has a blockchain in it, it immediately crosses the "too heavy" line for me.
Swarm would probably cross that line even without any of the blockchain stuff. It's more akin to Freenet than Bittorrent and would probably function better as a decentralized backend for most people. Expecting an average person to run a Swarm node is probably unrealistic in anything resembling its current form but allowing resilient decentralized sites which are accessible from any one of a number of gateways should be doable when/if they actually get around to implementing insured data storage that is the key component to the entire idea.
You're right about that, but I do wonder if this will be perfect for making distributed darknet marketplaces and torrent trackers a la what.cd.
No. It doesn't depend on blockchain except for the ENS resolution.