I can firmly say, although difficult, it is possible to tame the sheildhorns and razortooth on the golden age islands without the use of traps. Like people have said in other comments you need a good group with a clear plan and communication. We have tamed 6 razortooth now on EU official PvE and a handful of sheildhorns. So it can be done, were not exactly pro lol.
If trap building was enabled, them servers would be bogged down even more with structure spam on top of the insane amount of ships that are left at these islands. You can see us tame our very first razortooth in the link below if you would like an idea of what its like and how it goes without a trap :-)
https://www.youtube.com/watch?v=EnMS1xX_yGc