As I understand, SegWit allows anyone to create a SegWit address where they can send their bitcoins and transact from that wallet just as easily as they would with a traditional address. The SegWit inputs, however, would have a lower "weight", therefore they would appear smaller to the miners and thus would need lower fees to be included in a block. This would be despite the transaction itself being a bit bigger byte-wise due to the extra data required for the Witness part of the transaction.
So given all of that, is there any reason big Bitcoin companies that create a lot of transactions on daily basis wouldn't switch to SegWit addresses for the majority of their operations? It looks to me that if they would move their hot wallets onto SegWit addresses they could potentially cut down their transaction fees by a noticeable margin.
Is there any reason this isn't a standard way of doing things yet?