Most airlines now price the seat and the checked bag separately. The split is a pricing strategy with a cost-recovery argument attached to it.
Comparison shopping rewards the lowest headline number
Fares are overwhelmingly bought through search tools that rank by price. A carrier whose fare includes a bag appears more expensive than one whose fare does not.
Ranking position translates directly into bookings, so any element that can be removed from the headline number will be.
Once one carrier on a route unbundles, the others face a choice between matching or losing visibility. Matching is the usual outcome.
The cost argument is genuine but partial
Checked baggage does impose real costs: handling staff, sorting systems, loading time and fuel burned carrying the weight.
Those costs fall on the airline whether or not a particular passenger checks a bag, so charging the passengers who do use the service is defensible.
The fees charged, however, are set by what passengers will pay rather than by the underlying cost, which is why they vary so widely between carriers on identical routes.
The cabin bag became the pressure point
When checked bags carry a fee and cabin bags do not, passengers move their luggage into the cabin. Overhead space is finite and fills quickly.
Boarding slows, gate staff begin checking bags into the hold for free, and the airline loses both the fee and the turnaround time.
Many carriers responded by charging for the larger cabin bag as well, leaving only a small item free. That is a capacity management measure as much as a revenue one.
Why the fee rises at the airport
A bag declared at booking can be planned for. A bag presented at the gate has to be handled by staff who were doing something else.
The steep airport premium is designed to push the decision earlier rather than to price the handling, and it succeeds at that.
It also discourages passengers from gambling that their oversized item will pass unchallenged, which is what the fee structure is really aimed at.
What this does to the true price
The advertised fare has become a poor guide to what a trip costs, because the additions differ between carriers in both size and structure.
Some fare bundles include a bag, a seat and changes; others include nothing. The cheapest headline is frequently not the cheapest total.
Comparing like with like means pricing the whole trip as it will actually be flown, including every item the traveller will not be willing to leave behind.