They used to do the heater hose thing when I worked at the Exxon gas stations. The nice thing about it if you have people that tend to throw things into the can from any distance it protects the bag from pinch cuts against the edge of the can. No holes to leak when you pull it out. Inner tube and spoke bands work good too.
The absolute cheapest method is to do what every custodian does- tie a knot with the excess plastic bag...
I like the idea, would work good assuming the hose is a bit flexible and the garbage can is round. I noticed at my local park, the 'square w/ slightly rounded corners' cans,, they glued a few pieces of 3/4 pvc pipe into the shape of the inner lip, and that held the bag up (from the inside of the can) so the lid could still close.
I'm a janitor who works with the big plastic trashcans. I use 40" bungee cords. I tie knots in the cords till the tension is just right. Paid $.96 each for them on sale. off and on quickly. Try taking the heater hose off and on. see how easy or difficult it is.