If airliners profit by moving luggage from checked to carry-on, why do some LCC gate-check luggage?
A number of LCCs don't carry cargo at all or have a more limited cargo business, especially in Europe and the US. This is particularly the case if they're flying smaller narrowbody aircraft on shorter routes, where freight has to be bulk loaded. Ryanair and easyJet aren't in the freight business, though Southwest and AirAsia are. 

LCCs have strong motivations to reduce turnaround times and ensure maximum utilization of their aircraft. Freight can slow down operations (somebody has to get it to the gate on time, it has to be loaded/unloaded) and so can carry-on bags (everyone has to carry them, find a space for them, lift them, and once the bins are full, it takes time to collect the excess bags, tag them, and get them downstairs and into the hold). Getting passengers to gate-check bags early can help speed the boarding process. It's the gate agent's job to get the aircraft off on time, so they're motivated to gate-check bags before there's a problem fitting them in the overhead bins.

In addition, passengers find carry-on baggage convenient. You don't have to wait for it, don't have to worry about it getting lost, and you can access it during the flight. LCCs make extensive use of ancillary revenue, with a la carte airfares that involve extra charges for anything passengers might consider convenient, from a preferred seat to a beverage. As such, some airlines charge for carry-on bags (or disallow them on their cheapest fares), extracting more revenue from those who value this convenience and speeding the boarding process by reducing the number of carry-on bags.