SegWit does in fact represent a block size increase. It results in 1.7x the # of single-signature transactions per block and 4x the # of multi-signature transactions per block.

Unlimited block size? There are many reasons that's a very bad idea but here are a few:

1. It would put immense pressure on the network in terms of latency between miners, leading to less stable mining, a higher rate of reorganizations, and a massive advantage for the larger miners, resulting in increased mining centralization.

2. It would result in a substantial increase in the amount of bandwidth that each node has to handle. Modest increases are OK but unlimited blocks means the vast majority of nodes will die off. Remember that nodes have to check blocks as they come in, so this would be an insane DDoS vector. Imagine putting a funnel in someone's mouth instead of a straw and being able to force whatever you want in there.

3. It would result in a substantial increase in the amount of data that each node has to store. Remember that in Bitcoin 100% of data must be stored by 100% of nodes. Imagine "unlimited emails" with Gmail meant that you had to store all of the emails in the world for EVERYONE. Not a good idea.

That's not an increase in the size of the block per se, as much as it is an increase in the efficiency of encoding off-Blockchain information, no?

Not really. SegWit transactions are on-blockchain like any other - the only difference is that nodes which aren't keeping a full copy of the blockchain can save some extra space by discarding the witness part immediately after processing the block. (So I guess if you wanted to be pedantic you might be able to argue the witness part is off-blockchain in some sense, but even then the transfer of bitcoins still happens on the main blockchain.)

No, it is a space increase! Witness data is counted with a discount. Blocks can be larger than 1MB under SegWit.

Perhaps this is semantic?

The Core team scaling plan is to do a block size increase after SegWit.

Propagation times have been addressed by multiple technologies, including FIBRE (http://bitcoinfibre.org/).

You are correct and such proposals have been put forward: http://moneyandstate.com/thoughts-on-segwit2mb/

The Core team does not want blocksize increases.

They explicitly want prices to be high/number of transactions to be limited (think, supply and demand) .

This is because transaction "price" is equivalent to "amount of money spent on securing the blockchain".

> SegWit will allow more transactions to occur off chain

On-chain, actually. :-)