Eh? the NSA didn't pushed IDEA out, what pushed it is the fact that besides being actually substantially (esp. since 2013) less secure than AES and with poorer performance is that IDEA was a registered trademark and was under a full patent which meant implementing (prior to the patent expiration in 2012) was a nightmare.
I also hope that you don't insinuate that ECC was "invented" by UW since elliptic curve cryptography was known for quite a long time.
By the backdoor I assume you mean the whole NIST curves fiasco, well besides the fact that it was in use almost no where, if you speak to actual mathematicians you'll find out that it wasn't a big deal. The NIST curve was more about performance enchantment than backdooring, altough sadly for NIST and for the NSA it failed at providing both.
The big problems with ECC is that it's extremely susceptible to side channel attacks especially in embedded implementations, and that if you have the capability to use quantum computing for cryptanalysis then to break ECC you'll need only about 25-50% of the compute time/power than you would need to break RSA.
Also since ECC is asymmetric and quite resource consuming it's not really used in encryption as much as you think, sure it's good in any situation where you can use PKI but PKI is rarely used to encrypt actual data. The common uses of PKI are for authentication and initial key exchange data encryption whether it's in rest or in motion is usually based on symmetric encryption.