In order to come over this limitation, Pieter suggested to redesign bitcoin, where the hashes of all the signature goes into the coinbase. But still, without the original transaction data together with signature, you have no way to prove that the hashes are correct, you would still need all those data to prove the validity of each hash. However, those data would be in another chain, then it will reduce the data on main chain, but put the data into a side chain. And in future, that side chain will have all the capacity problem that bitcoin chain have today, even more difficult to deal with
1. Not a side chain, a parallel chain. For every header'ed block, there must be a corresponding SegWit block. Not a side chain.
2. SegWit chain is prunable. Future chain bloat not a problem. You haven't taken it all in yet (and neither have I)