But then you pay to check your bag, to select a seat, to print a boarding pass,to use a credit card, to get insurance if you are going to make any miniscule change to your itinerary (including moving the flight by a day), to get a bottle of water, and on and on.
Allegiant cuts costs by prohibiting transfers. Your total flight is the same as your stage length.
Indeed you pay to check your bag, but you don't need to. You can travel without a checked bag for free.
You pay to select a seat, but you don't need to. You can get one randomly assigned to you for free.
You pay to have a boarding card printed for you at the airport, but you don't need to. You can check-in online for free and print your own boarding card. You can even use your phone as a digital boarding card, doesn't cost anything.
You pay for making a change to your itinerary, but you don't need to. You should just make sure you enter the correct info upon booking. Of course you pay for moving the flight by a day which is very logical. You were expected on a certain flight, they kept a seat free for you on that flight. The pricing progress of that flight was based on the fact that you would be taking that flight and not another one.
You pay for a bottle of water, but you don't need to. You're not obliged to buy it, you could go without water for the length of the flight or you could bring your own water on board.
So the only additional costs on top of the ticket price that you need to make are credit card costs. In Europe, such costs are prohibited since there's no way of escaping them. Airlines are only allowed to charge for optional extras, and as you saw anything other than credit card costs are optional. You can go without if you want to. Before credit card costs were prohibited in Europe, most European LCCs had them too.
Just like Allegiant, most European LCCs also don't offer connections. For a long time Ryanair didn't offer connections, only recently they started offering them at a small selection of airports and basically they're arranged self-transfers. The ticket price is just the price of the two flights added up, no discount. In such, Allegiant is perhaps the most European of all American LCCs.