I recall flying in Europe and Britain in 1974, 1976, 1978, and 1986.
Getting model boxes on airliners was something of a hassle back then but still possible.
But considering covid, terrorism, and the profit motive today, it must be very near impossible.
If I was considering entering a contest via airline today, I would ship the model box via UPS, Fedex or Railway Express and not even mess with the airlines.