I use drinking straws, wood dowels, and cakes over 3 tiers I use foam core. I have never had a cake fall or shift - and I deliver cakes in one the the most challenging places to do so - San Francisco.
Correction - I have had one 4 tiered cake shift, but that was because it was the 2nd delivery of the day out of the city up in the mountains, that cake literally sat in my van for well over 2 hours before I got it where it needed to be. I know that cake was 100% fine until I had to go down a dirt driveway with probably an 8% downgrade and man-made dirt speed bumps. It shifted a fraction and cracked the SMBC on the bottom tier. All I had to to was push it back in place with a spatula and the cake was perfect.