Not exactly. Verification is needed because money transfers can be reversed (fraudulently, or legitimately in response to fraud), so remittance companies need to be reasonably sure to reduce fraud risk to an acceptable level.

However with Bitcoin there is no need for verification because a transfer is irreversible.

Cash-to-cash in under an hour would definitely be possible but only if I had immediate access to a Bitcoin ATM (I would "withdraw" directly to the recipient, by giving my ATM the recipient's ATM's deposit address)