This would be true even re-encoding to AVC. Recording, even hardware accelerated, is designed to use little compression and have good quality, so it can keep up

This would be true even re-encoding to AVC. Recording, even hardware accelerated, is designed to use little compression and have good quality, so it can keep up with the stream without slowing down your PC. The resulting bitrates are necessarily very high. Re-encoding more efficiently, without the realtime requirements, will usually yield good results.