Heh, no that’s not it at all. It isn’t because “they don’t know how much free space” it’s a weight and balance issue. They monitor the weight, fuel and depending on the flight load they rather gate check luggage to reduce it because usually later groups for Alaska board the back. The gate agent may say it’s space or whatnot, but that is a fib because imagine them trying to explain “weight and balance” to people all eager to get on a plane that can’t even leave until the door closes.
Balance issues involving passenger locations are solved by moving passengers (after the door closes and the manifest finalizes), not bags. Weight issues are solved by un-checking bags or bumping passengers. Checking bags for balance reasons is only done if there aren't enough checked bags to balance the contracted cargo, and is rare enough that it's generally called out as such.
Just like how they "monitor" weight by assuming average weights for simple categories and just counting passengers, many airlines let the computer decide when to cut it off based solely on the number of people boarded, times what they surveyed the average number of carryons per person to be, with zero feedback of whether the bins are actually filling up. Some airlines (American) go further and cut it off earlier than usual if the computer thinks D0 might be threatened.
Comical.