If BTC becomes so popular, 7 txs per second means it will be very rare in a world of billions of people to do on-chain transactions on a frequent basis.
Funnily enough, we'll replace the traditional banking system. And we'll do it with 7 transactions per second. 
I think BTC was designed for the average connection of 2009, which is a regular ADSL @ 1 Mbps (upload).
It doesn't matter, but I don't think it was. Satoshi had set the block size at 32 MB at first. By 2136 almost everyone will have FTTH, so block size could be increased with no repercussions.
There's already greater internet speed, but no such change. Perhaps it's just not worth the consensus inconvenience.