If only it was that simple. Signing the back designates a claimant, it doesn't mean they have rights to all the winnings. Office pools are a prime example.
And for instant winner terminal games, which some lotteries offer, a winning ticket may immediately print out of the terminal. In those instances, the player has no opportunity to sign the ticket until the lottery retailer hands it over to them. This is where trust is extra important, because the lottery retailer could claim the ticket wasn't yet paid for and/or refuse payment post win, and keep the winning ticket. Lottery agents generally are permitted to play the lottery, including at their own location. The player has an uphill climb in such a dispute unless they act quickly, including getting access to the surveillance video, assuming it even exists, before the retailer deletes it.
Utilizing a self-service terminal avoids many issues, and is generally safer for the player - less chance of disputes, since ticket only prints upon payment and the player gets immediate possession of the ticket. And lottery subscriptions are even safer yet, since that often cuts out the lottery agent completely.