Krusty,
Bf110s were not told to do that until the bomber losses were not dropping and were unsustainable. People keep acting like the close escort order was for the entire BoB, but it wasn't and the Bf110 did poorly before that as well.
I don't know about the 110C but specific to the 109E it WAS most of the BOB. The reason they had only 5 minutes over the target to fight was because they had to circle and form up and stay with the bomber formations as the bombers zig-zagged over France making their way in to the target. They had to rendevouz and if the timing was off they burned more gas waiting.
The Bf109 pilots could have and would have caused a lot more hurt to the RAF if they had just gone in in hunter killer mode and killed the RAF. The squadron leaders were practically begging for the freedom/permission to do so, but were not allowed.
I can only imagine 110C specific orders being just as strict.
P.S. Guppy I'm not saying it's a great plane, just that if you look at it from pure speed and alt, it's not without merit. Doctrine overruled capability. It has qualities the RAF wanted in their own aircraft, but were unable to produce in time. (i.e. whirlwind)