As far as I remember, the T/Cs were fitted to the B707 fleet because those early turbojets were liable to have contaminated bleed air - oil sealing wasn't all that good then. The engines were more than capable of supplying adequate bleed air for pressurisation needs. Remember that the T/Cs extracted much more bleed energy to operate than an equivalent straight bleed flow.
Taily, the extra air doors around the nose cowl were, in fact, known in Boeing-speak as "secondary air inlet doors". Remember that the inlet should be sized for the cruise, so then it will be too small at low airspeeds and engine efficiency will improve with more air. The JT3D nose cowl doors were still a bit open till well up the climb. Again your memory serves you well - early JT9s had them and I personally loved the howl. Nose cowls were all sealed up to help keep the noise down and make us better neighbours, but the old JT9 nose cowls made it easy to set thrust for T/O.