To answer your question more specifically, what you are seeing is often called Fast Pay or Quick pay. Imagine a fast food drive thru trying to get signatures back during the lunch rush, not a good idea as far as speed of service goes.
That said, Visa and MasterCard both have limits on what they will accept as fast pay transactions due to risk. The limit for each is different, but both are around $50 IIRC. Many businesses will enable fast pay for anything under $30 or so just to save time.
The actual terminal that cards are run through can be set to different limits for fast pay, but the merchant is always at risk.
Say you go into Costco and pay for $20 worth of goods. They don’t have you sign because it’s a low amount, and they want speed of service. If you dispute that charge, they would be asked for a signed copy of the receipt, and any other documentation associated with the sale. You never signed anything, so that makes it a bit harder for them to defend their end of the transaction.
Your were using an Amex card too. They operate on their own set of rules. Only recently did Discover change over to a “bank-card” type of processing. They are now treated more or less like Visa and MasterCard in some senses.
Amex does what they want. Period. They issue separate deposits to merchant accounts from the other card types, will not speak with ISO’s or merchant acquirers on behalf of a merchant. You can bet that the $100 transaction limit shifts the risk to either the merchant or the card holder. Amex does what they want. Period. They’re also the only company that wants you to pay a full balance every month. Visa and MasterCard thrive off of late fees and other charges.