I'm sure there will be various views on this, so I'll just offer my experience which is emphatically not advice!

Putting bikes in a solid bike case, like the 'pro-case' I have - expensive in airline charges as the case, even without anything inside, is an economy ticket's weight allowance. However, in my experience, the bike has arrived safe

Putting bike in a cardboard carton such as those obtainable from a bike shop or an airline terminal - no additional airline charge, and in each of 5 journeys a badly damaged bike. Plaited forks, gearsets kicked horizontal, spokesets whisked. Wouldn't do it again

Bike recognisably a bike inside transparent bubble wrap with pedals removed and re-installed on the inside, and handlebars turned 90 degrees in line with the top tube - no charges, no damage, the handlers seemed to respect and recognise what they were handling

My Xoortr Swift folded until it fitted in a newspaper filled dive bag - not the slightest issue!